Question 1

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = 6x3 - 5x2 + 6x - 6.

Accepted Answer

A)  3 positive reals or 1 positive real;3 negative reals or 1 negative real
B)  no positive reals;no negative reals
C)  3 positive reals or 1 positive real;1 negative real
D)  1 positive real;3 negative reals or 1 negative real
E)  3 positive reals or 1 positive real;no negative realsF) B) and D)
G) B) and C)

Question 2

Find all the zeros of the function and write the polynomial as a product of linear factors. ​
X4 + 13x2 + 36
​

Accepted Answer

A)  ±3i,±2i; (x + 3i) (x - 3i) (x + 2) (x - 2) 
B)  ±3i,±2i; (x + 3i) (x - 3i) (x + 2i) (x - 2i) 
C)  -3i,-2i; (x - 3i) (x - 3i) (x - 2i) (x - 2i) 
D)  3i,2i; (x + 3i) (x + 3i) (x + 2i) (x + 2i) 
E)  ±3i,±2i; (x + 3) (x - 3) (x + 2i) (x - 2i) F) A) and C)
G) All of the above

Question 3

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = x5 + 2x.

Accepted Answer

A)  1 positive real;3 negative reals or 1 negative real
B)  no positive reals;no negative reals
C)  1 positive real;5 negative reals or 3 negative reals or 1 negative real
D)  5 positive reals or 3 positive reals or 1 positive real;no negative reals
E)  3 positive reals or 1 positive real;3 negative reals or 1 negative realF) A) and B)
G) C) and D)

Question 4

Use the given zero to find all the zeros of the function. ?
Function Zero
7x3 + 8x2 + 175x + 200 5i
?
?

Accepted Answer

A)  ±5i,  87\frac { 8 } { 7 }78​ 
B)  ±5i,  −87- \frac { 8 } { 7 }−78​ 
C)  ±5i,-8
D)  ±5i,  −78- \frac { 7 } { 8 }−87​ 
E)  ±5i,  ±87i\pm \frac { 8 } { 7 } i±78​iF) A) and C)
G) C) and D)

Question 5

Given -3i is a root,determine all other roots of f(x) = x3 + 2x2 + 9x + 18.

Accepted Answer

A)  x = ±2,3i
B)  x = -3,±2i
C)  x = -2,±3
D)  x = -2,3i
E)  x = ±2,3F) B) and D)
G) D) and E)

Question 6

Use the given zero to find all the zeros of the function. ​
Function Zero
X3 + 13x2 + 59x + 87 -5 - 2i
​
​

Accepted Answer

A)  3,5 ± 2i
B)  ±3i,-5 ± 2i
C)  -3,5 ± 2i
D)  -3,-5 ± 2i
E)  3,-5 ± 2iF) B) and C)
G) None of the above

Question 7

Find all the rational zeros of the function. ​
X3 + 18x2 + 105x + 200
​

Accepted Answer

A)  -8,5
B)  5,8
C)  -8,-5
D)  -8,-5,5
E)  -5,8F) A) and D)
G) A) and E)

Question 8

Given -6i is a root,determine all other roots of f(x) = x3 + 2x2 + 36x + 72. ​

Accepted Answer

A)  x = -2,±6
B)  x = -2,6i
C)  x = -6,±2i
D)  x = ±2,6i
E)  x = ±2,6F) A) and D)
G) B) and D)

Question 9

Find all real solutions of the polynomial equation x4 - 7x3 + 42x - 36 = 0. ?
?

Accepted Answer

A)  x = 1,6,  ±6\pm \sqrt { 6 }±6c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)  x = 1,36
C)  x = 1,  ±6\pm \sqrt { 6 }±6c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)  x = 1,-7,-6
E)  x = 1,-36,12 F) B) and E)
G) None of the above

Question 10

Find a polynomial function with real coefficients that has the given zeros. ​
1,3i
​

Accepted Answer

A)  x3 - x2 - 9x - 9
B)  x3 + x2 + 9x - 9
C)  x3 - x2 + 9x - 9
D)  x3 + x2 + 9x + 9
E)  x3 - x2 + 9x + 9F) A) and E)
G) B) and C)

Question 11

Find all the zeros of the function and write the polynomial as a product of linear factors. ​
X2 + 49
​

Accepted Answer

A)  7i; (x + 7i) (x - 7i) 
B)  -7i; (x + 7i) (x - 7i) 
C)  ±7i; (x + 7) (x - 7) 
D)  -7i; (x + 7) (x - 7) 
E)  ±7i; (x + 7i) (x - 7i) F) B) and E)
G) A) and D)

Question 12

Find a polynomial function with real coefficients that has the given zeros. ​
6,2 + i
​

Accepted Answer

A)  x3 - 10x2 - 29x - 30
B)  x3 + 10x2 + 29x - 30
C)  x3 - 10x2 + 29x - 30
D)  x3 - 10x2 + 29x + 30
E)  x3 + 10x2 + 29x + 30F) A) and E)
G) B) and E)

Question 13

Write f(x) = x3 - 5x2 + 16x - 80 as a product of linear factors.

Accepted Answer

A)  f(x) = (x - 5) (x - 4) 2
B)  f(x) = (x - 5) (x + 4i) (x - 4i) 
C)  f(x) = (x - 5) 2(x - 4i) 
D)  f(x) = (x - 5) (x + 4) 2
E)  f(x) = (x + 5) (x - 5) (x + 4) F) B) and C)
G) C) and D)

Question 14

Find all the real zeros of f(x) = 4x3 - 12x2 - 15x - 4.

Accepted Answer

A)  x =  14\frac { 1 } { 4 }41​  ,2
B)  x =  −12- \frac { 1 } { 2 }−21​  ,  −14- \frac { 1 } { 4 }−41​ 
C)  x =  12\frac { 1 } { 2 }21​  ,  −14- \frac { 1 } { 4 }−41​ 
D)  x =  −12- \frac { 1 } { 2 }−21​  ,4
E)  x =  −12- \frac { 1 } { 2 }−21​  ,-4 F) A) and B)
G) B) and D)

Question 15

Write the polynomial as the product of factors that are irreducible over the rationals. ?
F(x) = x4 + 6x2 - 27
?

Accepted Answer

A)    (x2+9) (x4−3) \left( x ^ { 2 } + 9 \right)  \left( x ^ { 4 } - 3 \right) (x2+9) (x4−3)  
B)    (x2+9) (x2−3) \left( x ^ { 2 } + 9 \right)  \left( x ^ { 2 } - 3 \right) (x2+9) (x2−3)  
C)    (x+9) (x2−3) ( x + 9 )  \left( x ^ { 2 } - 3 \right) (x+9) (x2−3)  
D)    (x+6) (x2−3) ( x + 6 )  \left( x ^ { 2 } - 3 \right) (x+6) (x2−3)  
E)    (x2+9) (x+3) (x+3) \left( x ^ { 2 } + 9 \right)  ( x + \sqrt { 3 } )  ( x + \sqrt { 3 } ) (x2+9) (x+3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​) (x+3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​) F) None of the above
G) B) and E)

Question 16

Write the polynomial in completely factored form. ?
F(x) = x4 + 20x2 - 125
?

Accepted Answer

A)    (x+5) (x−5) (x+5) (x−5) ( x + 5 )  ( x - 5 )  ( x + \sqrt { 5 } )  ( x - \sqrt { 5 } ) (x+5) (x−5) (x+5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​) (x−5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​)  
B)    (x+5) (x−5i) (x+5) (x−5i) ( x + 5 )  ( x - 5 i )  ( x + \sqrt { 5 } )  ( x - \sqrt { 5 } i ) (x+5) (x−5i) (x+5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​) (x−5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​i)  
C)    (x+5) (x−5) (x+5i) (x−5i) ( x + 5 )  ( x - 5 )  ( x + \sqrt { 5 } i )  ( x - \sqrt { 5 } i ) (x+5) (x−5) (x+5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​i) (x−5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​i)  
D)    (x+5i) (x−5i) (x+5) (x−5) ( x + 5 i )  ( x - 5 i )  ( x + \sqrt { 5 } )  ( x - \sqrt { 5 } ) (x+5i) (x−5i) (x+5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​) (x−5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​)  
E)    (x+5i) (x−5) (x+5i) (x−5) ( x + 5 i )  ( x - 5 )  ( x + \sqrt { 5 i } )  ( x - \sqrt { 5 } ) (x+5i) (x−5) (x+5ic-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​) (x−5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​) F) A) and E)
G) B) and D)

Question 17

Find all real solutions of the polynomial equation 6x6 + x5 + 29x4 + 5x3 + 19x2 + 4x - 4 = 0.

Accepted Answer

A)  x =  13\frac { 1 } { 3 }31​  ,  −12- \frac { 1 } { 2 }−21​  ,±1
B)  x =  −13- \frac { 1 } { 3 }−31​  ,  12\frac { 1 } { 2 }21​  ,±2
C)  x =  13\frac { 1 } { 3 }31​  ,  −12- \frac { 1 } { 2 }−21​ 
D)  x = ±  13\frac { 1 } { 3 }31​  ,±  12\frac { 1 } { 2 }21​  ,±1
E)  x = ±  13\frac { 1 } { 3 }31​  ,±  12\frac { 1 } { 2 }21​  ,±2 F) A) and D)
G) C) and D)

Question 18

Find all zeros of the function f(x) = (x - 4) (x + 3) [x + (4 + 3i) ][x - (4 - 3i) ].

Accepted Answer

A)  x = 4,-3,-4 - 3i,4 - 3i
B)  x = -4,3,4 - 3i,4 + 3i
C)  x = -4,3,4 + 3i,-4 - 3i
D)  x = 4,-3,4 + 3i,-4 + 3i
E)  x = 4,-3,-4 - 3i,4 + 3iF) B) and E)
G) A) and D)

Question 19

Given 3 + i is a root,determine all other roots of f(x) = x4 - 12x3 + 59 x2 - 138x + 130.

Accepted Answer

A)  x = 3 - i,3 ± 2i
B)  x = 3 - i,2 ± 3i
C)  x = 3 + i,3 ± 2i​,2 - i
D)  x = 3 - i,2 ± i
E)  x = 3 - i,3 - 2i​,2 - iF) C) and E)
G) C) and D)

Question 20

Find all zeros of the function f(x) = x2(x + 1) (x3 - 64) .

Accepted Answer

A)  x = 0,1,-4
B)  x = 0,-1,4
C)  x = -1,64
D)  x = 1,-64
E)  x = 0,-1,4,  −2−23i- 2 - 2 \sqrt { 3 } i−2−23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​i  ,  −2+23i- 2 + 2 \sqrt { 3 } i−2+23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​iF) None of the above
G) B) and E)

Exam 15: Zeros of Polynomial Functions

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = 6x3 - 5x2 + 6x - 6.

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Write the polynomial in completely factored form. ? F(x) = x4 + 20x2 - 125 ?

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Find all real solutions of the polynomial equation 6x6 + x5 + 29x4 + 5x3 + 19x2 + 4x - 4 = 0.

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Use the given zero to find all the zeros of the function. ? Function Zero 7x3 + 8x2 + 175x + 200 5i ? ?

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Find a polynomial function with real coefficients that has the given zeros. ​ 6,2 + i ​

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Use the given zero to find all the zeros of the function. ​ Function Zero X3 + 13x2 + 59x + 87 -5 - 2i ​ ​

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Find all zeros of the function f(x) = x2(x + 1) (x3 - 64) .

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Write f(x) = x3 - 5x2 + 16x - 80 as a product of linear factors.

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Find all the zeros of the function and write the polynomial as a product of linear factors. ​ X2 + 49 ​

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Find all real solutions of the polynomial equation x4 - 7x3 + 42x - 36 = 0. ? ?

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Find all zeros of the function f(x) = (x - 4) (x + 3) [x + (4 + 3i) ][x - (4 - 3i) ].

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Find a polynomial function with real coefficients that has the given zeros. ​ 1,3i ​

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Write the polynomial as the product of factors that are irreducible over the rationals. ? F(x) = x4 + 6x2 - 27 ?

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Given -3i is a root,determine all other roots of f(x) = x3 + 2x2 + 9x + 18.

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Given -6i is a root,determine all other roots of f(x) = x3 + 2x2 + 36x + 72. ​

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Find all the real zeros of f(x) = 4x3 - 12x2 - 15x - 4.

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Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = x5 + 2x.

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Find all the rational zeros of the function. ​ X3 + 18x2 + 105x + 200 ​

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Find all the zeros of the function and write the polynomial as a product of linear factors. ​ X4 + 13x2 + 36 ​

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Given 3 + i is a root,determine all other roots of f(x) = x4 - 12x3 + 59 x2 - 138x + 130.

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Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = 6x³ - 5x² + 6x - 6.

Correct Answer
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Write the polynomial in completely factored form. ? F(x) = x⁴ + 20x² - 125 ?

Correct Answer
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Find all real solutions of the polynomial equation 6x⁶ + x⁵ + 29x⁴ + 5x³ + 19x² + 4x - 4 = 0.

Correct Answer
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Use the given zero to find all the zeros of the function. ? Function Zero 7x³ + 8x² + 175x + 200 5i ? ?

Correct Answer
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Find a polynomial function with real coefficients that has the given zeros. 6,2 + i

Correct Answer
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Use the given zero to find all the zeros of the function. Function Zero X³ + 13x² + 59x + 87 -5 - 2i

Correct Answer
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Find all zeros of the function f(x) = x²(x + 1) (x³ - 64) .

Correct Answer
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Write f(x) = x³ - 5x² + 16x - 80 as a product of linear factors.

Correct Answer
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Find all the zeros of the function and write the polynomial as a product of linear factors. X² + 49

Correct Answer
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Find all real solutions of the polynomial equation x⁴ - 7x³ + 42x - 36 = 0. ? ?

Correct Answer
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Correct Answer
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Find a polynomial function with real coefficients that has the given zeros. 1,3i

Correct Answer
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Write the polynomial as the product of factors that are irreducible over the rationals. ? F(x) = x⁴ + 6x² - 27 ?

Correct Answer
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Given -3i is a root,determine all other roots of f(x) = x³ + 2x² + 9x + 18.

Correct Answer
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Given -6i is a root,determine all other roots of f(x) = x³ + 2x² + 36x + 72.

Correct Answer
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Find all the real zeros of f(x) = 4x³ - 12x² - 15x - 4.

Correct Answer
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Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x) = x⁵ + 2x.

Correct Answer
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Find all the rational zeros of the function. X³ + 18x² + 105x + 200

Correct Answer
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Find all the zeros of the function and write the polynomial as a product of linear factors. X⁴ + 13x² + 36

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Given 3 + i is a root,determine all other roots of f(x) = x⁴ - 12x³ + 59 x² - 138x + 130.

Correct Answer
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