Question 1

Find the product. Assume all variable exponents represent whole numbers.
-$$\left( x ^ { 2 } + x + 3 \right) \left( x ^ { 2 } + x + 6 \right)$$

Accepted Answer

A)  $x ^ { 4 } + x ^ { 3 } + 9 x ^ { 2 } + 9 x + 18$ 
B)  $x ^ { 4 } + x ^ { 3 } - 8 x ^ { 2 } - 9 x + 18$ 
C)  $x ^ { 4 } + 2 x ^ { 3 } + 10 x ^ { 2 } + 9 x + 18$ 
D)  $x ^ { 4 } + 2 x ^ { 3 } - 9 x ^ { 2 } - 3 x + 18$ 
A)  $x ^ { 4 } + x ^ { 3 } + 9 x ^ { 2 } + 9 x + 18$ 
B)  $x ^ { 4 } + x ^ { 3 } - 8 x ^ { 2 } - 9 x + 18$ 
C)  $x ^ { 4 } + 2 x ^ { 3 } + 10 x ^ { 2 } + 9 x + 18$ 
D)  $x ^ { 4 } + 2 x ^ { 3 } - 9 x ^ { 2 } - 3 x + 18$ C

Question 2

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers.
-$\left( y ^ { 3 } - 7 \right) \left( y ^ { 3 } + 7 \right)$

Accepted Answer

A)  $y ^ { 6 } - 14$ 
B)  $y ^ { 9 } - 49$ 
C)  $y ^ { 9 } - 14$ 
D)  $y ^ { 6 } - 49$ 
A)  $y ^ { 6 } - 14$ 
B)  $y ^ { 9 } - 49$ 
C)  $y ^ { 9 } - 14$ 
D)  $y ^ { 6 } - 49$ D

Question 3

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
-$$[ ( 3 x - 4 ) + 2 y ] ^ { 2 }$$

Accepted Answer

A)  $9 x ^ { 2 } - 12 x + 16 + 6 x y + 8 y + 4 y ^ { 2 }$ 
B)  $9 x ^ { 2 } - 24 x + 16 + 6 x y + 8 y + 4 y ^ { 2 }$ 
C)  $9 x ^ { 2 } - 24 x + 16 + 12 x y - 16 y + 4 y ^ { 2 }$ 
D)  $9 x ^ { 2 } - 24 x + 12 x y - 16 y + 4 y ^ { 2 }$ 
A)  $9 x ^ { 2 } - 12 x + 16 + 6 x y + 8 y + 4 y ^ { 2 }$ 
B)  $9 x ^ { 2 } - 24 x + 16 + 6 x y + 8 y + 4 y ^ { 2 }$ 
C)  $9 x ^ { 2 } - 24 x + 16 + 12 x y - 16 y + 4 y ^ { 2 }$ 
D)  $9 x ^ { 2 } - 24 x + 12 x y - 16 y + 4 y ^ { 2 }$ C

Question 4

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
-$12 x ^ { 9 } y ^ { 8 } + 54 x ^ { 2 } y ^ { 6 } + 54 x ^ { 6 } y ^ { 4 }$

Accepted Answer

A)  $6 x ^ { 2 } \left( 2 x ^ { 7 } y ^ { 8 } + 9 y ^ { 6 } + 9 x ^ { 4 } y ^ { 4 } \right)$ 
B)  $x ^ { 2 } y ^ { 4 } \left( 12 x ^ { 7 } y ^ { 4 } + 54 y ^ { 2 } + 54 x ^ { 4 } \right)$ 
C)  $6 \left( 2 x ^ { 9 } y ^ { 8 } + 9 x ^ { 2 } y ^ { 6 } + 9 x ^ { 6 } y ^ { 4 } \right)$ 
D)  $6 x ^ { 2 } y ^ { 4 } \left( 2 x ^ { 7 } y ^ { 4 } + 9 y ^ { 2 } + 9 x ^ { 4 } \right)$ 
A)  $6 x ^ { 2 } \left( 2 x ^ { 7 } y ^ { 8 } + 9 y ^ { 6 } + 9 x ^ { 4 } y ^ { 4 } \right)$ 
B)  $x ^ { 2 } y ^ { 4 } \left( 12 x ^ { 7 } y ^ { 4 } + 54 y ^ { 2 } + 54 x ^ { 4 } \right)$ 
C)  $6 \left( 2 x ^ { 9 } y ^ { 8 } + 9 x ^ { 2 } y ^ { 6 } + 9 x ^ { 6 } y ^ { 4 } \right)$ 
D)  $6 x ^ { 2 } y ^ { 4 } \left( 2 x ^ { 7 } y ^ { 4 } + 9 y ^ { 2 } + 9 x ^ { 4 } \right)$

Question 5

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
-$$\left( a ^ { n } + 3 b ^ { n } \right) ^ { 2 }$$

Accepted Answer

A)  $a ^ { 2 n } + 6 a ^ { n } b ^ { n } + 9 b ^ { 2 n }$ 
B)  $a ^ { n } + 6 a ^ { n } b ^ { n } + 9 b ^ { n }$ 
C)  $a ^ { n + 2 } + 6 a ^ { n } b ^ { n } + 9 b ^ { n + 2 }$ 
D)  $a ^ { 2 n } + 3 a ^ { n } b ^ { n } + 9 b ^ { 2 n }$ 
A)  $a ^ { 2 n } + 6 a ^ { n } b ^ { n } + 9 b ^ { 2 n }$ 
B)  $a ^ { n } + 6 a ^ { n } b ^ { n } + 9 b ^ { n }$ 
C)  $a ^ { n + 2 } + 6 a ^ { n } b ^ { n } + 9 b ^ { n + 2 }$ 
D)  $a ^ { 2 n } + 3 a ^ { n } b ^ { n } + 9 b ^ { 2 n }$

Question 6

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
-$$\left( 11 x y ^ { 2 } - x y \right) ^ { 2 }$$

Accepted Answer

A)  $11 x ^ { 2 } y ^ { 4 } - 22 x ^ { 2 } y ^ { 3 } + x ^ { 2 } y ^ { 2 }$ 
B)  $121 x ^ { 2 } y ^ { 4 } - 22 x ^ { 2 } y ^ { 3 } + x ^ { 2 } y ^ { 2 }$ 
C)  $121 x ^ { 2 } y ^ { 4 } - 11 x ^ { 2 } y ^ { 3 } + x ^ { 2 } y ^ { 2 }$ 
D)  $121 x ^ { 2 } y ^ { 2 } - 22 x ^ { 2 } y ^ { 3 } + x ^ { 2 } y ^ { 2 }$ 
A)  $11 x ^ { 2 } y ^ { 4 } - 22 x ^ { 2 } y ^ { 3 } + x ^ { 2 } y ^ { 2 }$ 
B)  $121 x ^ { 2 } y ^ { 4 } - 22 x ^ { 2 } y ^ { 3 } + x ^ { 2 } y ^ { 2 }$ 
C)  $121 x ^ { 2 } y ^ { 4 } - 11 x ^ { 2 } y ^ { 3 } + x ^ { 2 } y ^ { 2 }$ 
D)  $121 x ^ { 2 } y ^ { 2 } - 22 x ^ { 2 } y ^ { 3 } + x ^ { 2 } y ^ { 2 }$

Question 7

Give the requested components for the polynomial.
-$x ^ { 5 } - 2 x ^ { 4 } y ^ { 8 } + 11 x y - 7 x + 9$; degree of each term and degree of the polynomial

Accepted Answer

A)  degrees: $5,12,2,1$, 0; degree of polynomial: 12 
B)  degrees: $5,4,2,0$; degree of polynomial: 19 
C)  degrees: $1 , - 2,11 , - 7,9$; degree of polynomial: $- 2$ 
D)  degrees: $5,4,1,1,0$; degree of polynomial: 5 
A)  degrees: $5,12,2,1$, 0; degree of polynomial: 12 
B)  degrees: $5,4,2,0$; degree of polynomial: 19 
C)  degrees: $1 , - 2,11 , - 7,9$; degree of polynomial: $- 2$ 
D)  degrees: $5,4,1,1,0$; degree of polynomial: 5

Question 8

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
-$$( 5 x + 3 y ) ^ { 2 }$$

Accepted Answer

A)  $25 x ^ { 2 } + 9 y ^ { 2 }$ 
B)  $5 x ^ { 2 } + 30 x y + 9 y ^ { 2 }$ 
C)  $5 x ^ { 2 } + 9 y ^ { 2 }$ 
D)  $25 x ^ { 2 } + 30 x y + 9 y ^ { 2 }$ 
A)  $25 x ^ { 2 } + 9 y ^ { 2 }$ 
B)  $5 x ^ { 2 } + 30 x y + 9 y ^ { 2 }$ 
C)  $5 x ^ { 2 } + 9 y ^ { 2 }$ 
D)  $25 x ^ { 2 } + 30 x y + 9 y ^ { 2 }$

Question 9

Subtract the polynomials. Assume all variable exponents represent whole numbers.
-$$\left( 2 x ^ { 2 n } - 7 x ^ { n } - 19 \right) - \left( 9 x ^ { 2 n } - 5 x ^ { n } + 13 \right)$$

Accepted Answer

A)  $- 7 x ^ { 2 n } - 2 x ^ { n } - 6$ 
B)  $- 7 x ^ { 2 n } + 2 x ^ { n } - 6$ 
C)  $- 7 x ^ { 2 n } - 2 x ^ { n } - 32$ 
D)  $- 7 x ^ { 4 n } - 2 x ^ { 2 n } - 32$ 
A)  $- 7 x ^ { 2 n } - 2 x ^ { n } - 6$ 
B)  $- 7 x ^ { 2 n } + 2 x ^ { n } - 6$ 
C)  $- 7 x ^ { 2 n } - 2 x ^ { n } - 32$ 
D)  $- 7 x ^ { 4 n } - 2 x ^ { 2 n } - 32$

Question 10

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
-$$42 x ^ { 3 } y + 54 x y ^ { 6 }$$

Accepted Answer

A)  $6 y \left( 7 x ^ { 3 } + 9 x y ^ { 5 } \right)$ 
B)  $6 x y \left( 7 x ^ { 2 } + 9 y ^ { 5 } \right)$ 
C)  $6 x \left( 7 x ^ { 2 } y + 9 y ^ { 6 } \right)$ 
D)  $x y \left( 42 x ^ { 2 } + 54 y ^ { 5 } \right)$ 
A)  $6 y \left( 7 x ^ { 3 } + 9 x y ^ { 5 } \right)$ 
B)  $6 x y \left( 7 x ^ { 2 } + 9 y ^ { 5 } \right)$ 
C)  $6 x \left( 7 x ^ { 2 } y + 9 y ^ { 6 } \right)$ 
D)  $x y \left( 42 x ^ { 2 } + 54 y ^ { 5 } \right)$

Question 11

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
-$$( x + y + 12 ) ^ { 2 }$$

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } + 24 x + 24 y + 144$ 
B)  $x ^ { 2 } + y ^ { 2 } + 144$ 
C)  $x ^ { 2 } + 2 x y + y ^ { 2 } + 24 x + 24 y + 144$ 
D)  $x ^ { 2 } + 2 x y + y ^ { 2 } + 144$ 
A)  $x ^ { 2 } + y ^ { 2 } + 24 x + 24 y + 144$ 
B)  $x ^ { 2 } + y ^ { 2 } + 144$ 
C)  $x ^ { 2 } + 2 x y + y ^ { 2 } + 24 x + 24 y + 144$ 
D)  $x ^ { 2 } + 2 x y + y ^ { 2 } + 144$

Question 12

Add the polynomials. Assume all variable exponents represent whole numbers.
-$$\left( 4 x ^ { 6 } - 8 x ^ { 4 } + 8 x \right) + \left( 5 x ^ { 6 } - 2 x ^ { 4 } + 5 x \right)$$

Accepted Answer

A)  $9 x - 10 x ^ { 6 } + 13 x ^ { 4 }$ 
B)  $13 x ^ { 6 } + 2 x ^ { 4 } - 3 x$ 
C)  $12 x ^ { 11 }$ 
D)  $9 x ^ { 6 } - 10 x ^ { 4 } + 13 x$ 
A)  $9 x - 10 x ^ { 6 } + 13 x ^ { 4 }$ 
B)  $13 x ^ { 6 } + 2 x ^ { 4 } - 3 x$ 
C)  $12 x ^ { 11 }$ 
D)  $9 x ^ { 6 } - 10 x ^ { 4 } + 13 x$

Question 13

Add the polynomials. Assume all variable exponents represent whole numbers.
-$$\left( 2 x ^ { 9 } - 6 x ^ { 8 } - 7 x ^ { 7 } - 8 \right) + \left( 4 x ^ { 9 } + 8 x ^ { 8 } + 3 x ^ { 7 } + 4 \right)$$

Accepted Answer

A)  $6 x ^ { 18 } + 2 x ^ { 16 } - 4 x ^ { 14 } - 4$ 
B)  $0 x ^ { 9 } + 0 x ^ { 8 } + 6 x ^ { 7 } - 2$ 
C)  $6 x ^ { 9 } + 2 x ^ { 8 } - 4 x ^ { 7 } - 4$ 
D)  $4 x ^ { 48 } - 4$ 
A)  $6 x ^ { 18 } + 2 x ^ { 16 } - 4 x ^ { 14 } - 4$ 
B)  $0 x ^ { 9 } + 0 x ^ { 8 } + 6 x ^ { 7 } - 2$ 
C)  $6 x ^ { 9 } + 2 x ^ { 8 } - 4 x ^ { 7 } - 4$ 
D)  $4 x ^ { 48 } - 4$

Question 14

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
-$$( x - 10 y ) ( 4 x - 3 y )$$

Accepted Answer

A)  $4 x ^ { 2 } - 43 x y - 30 y ^ { 2 }$ 
B)  $4 x ^ { 2 } - 43 x y + 13 y ^ { 2 }$ 
C)  $4 x ^ { 2 } - 43 x y + 30 y ^ { 2 }$ 
D)  $4 x ^ { 2 } + 43 x y + 30 y ^ { 2 }$ 
A)  $4 x ^ { 2 } - 43 x y - 30 y ^ { 2 }$ 
B)  $4 x ^ { 2 } - 43 x y + 13 y ^ { 2 }$ 
C)  $4 x ^ { 2 } - 43 x y + 30 y ^ { 2 }$ 
D)  $4 x ^ { 2 } + 43 x y + 30 y ^ { 2 }$

Question 15

Give the requested components for the polynomial.
-$- 5 x ^ { 3 } + 6 x ^ { 2 } + 4 x$; the degree of the polynomial and the leading coefficient of the polynomial.

Accepted Answer

A)  degrees: 3,2 , and 1 ; coefficients: $- 5,6$, and 4 
B)  degree: $- 5$; coefficient: 3 
C)  degree: 3 ; coefficient: $- 5$ 
D)  degrees: $- 5,6$, and 4 ; coefficients: 3,2 , and 0 
A)  degrees: 3,2 , and 1 ; coefficients: $- 5,6$, and 4 
B)  degree: $- 5$; coefficient: 3 
C)  degree: 3 ; coefficient: $- 5$ 
D)  degrees: $- 5,6$, and 4 ; coefficients: 3,2 , and 0

Question 16

Solve the problem.
-Find the area of the rectangle by multiplying the length and the width of the large rectangle using the FOIL method.

Accepted Answer

A)  $x ^ { 2 } + 63$ 
B)  $x ^ { 2 } + 16 x$ 
C)  $x ^ { 2 } + 16 x + 63$ 
D)  $x ^ { 2 } + 32 x + 63$ 
A)  $x ^ { 2 } + 63$ 
B)  $x ^ { 2 } + 16 x$ 
C)  $x ^ { 2 } + 16 x + 63$ 
D)  $x ^ { 2 } + 32 x + 63$

Question 17

Give the requested components for the polynomial.
-$5 x ^ { 8 } y + x ^ { 7 } y ^ { 3 } + 13 y ^ { 2 }$; leading term and leading coefficient of the polynomial

Accepted Answer

A)  leading term: $5 x ^ { 8 } y$; leading coefficient: 5 
B)  leading term: $x ^ { 7 } y ^ { 3 }$; leading coefficient: 1 
C)  leading term: $13 y ^ { 2 }$; leading coefficient: 13 
D)  leading term: $\mathrm { x } ^ { 7 } \mathrm { y } ^ { 3 }$; leading coefficient: 13 
A)  leading term: $5 x ^ { 8 } y$; leading coefficient: 5 
B)  leading term: $x ^ { 7 } y ^ { 3 }$; leading coefficient: 1 
C)  leading term: $13 y ^ { 2 }$; leading coefficient: 13 
D)  leading term: $\mathrm { x } ^ { 7 } \mathrm { y } ^ { 3 }$; leading coefficient: 13

Question 18

Add the polynomials. Assume all variable exponents represent whole numbers.
-$$\left( 5 x ^ { 2 n } - x ^ { n } - 1 \right) + \left( x ^ { 2 n } + 4 x ^ { n } + 10 \right)$$

Accepted Answer

A)  $4 x ^ { 4 n } - 5 x ^ { 2 n } - 11$ 
B)  $6 x ^ { 2 n } + 3 x ^ { n } + 9$ 
C)  $5 x ^ { 2 n } + 4 x ^ { n } + 10$ 
D)  $6 x ^ { 4 n } + 5 x ^ { 2 n } + 11$ 
A)  $4 x ^ { 4 n } - 5 x ^ { 2 n } - 11$ 
B)  $6 x ^ { 2 n } + 3 x ^ { n } + 9$ 
C)  $5 x ^ { 2 n } + 4 x ^ { n } + 10$ 
D)  $6 x ^ { 4 n } + 5 x ^ { 2 n } + 11$

Question 19

Add the polynomials. Assume all variable exponents represent whole numbers.
-$$\left( - 9 x ^ { 7 } + 18 x ^ { 6 } - 13 \right) + \left( 3 x ^ { 7 } + 16 x ^ { 6 } - 9 \right)$$

Accepted Answer

A)  $- 6 x ^ { 7 } + 34 x ^ { 6 } - 22$ 
B)  $6 \times 13$ 
C)  $- 6 x ^ { 7 } + 25 x ^ { 6 } + 4$ 
D)  $- 6 x ^ { 7 } + 34 x ^ { 6 } + 4$ 
A)  $- 6 x ^ { 7 } + 34 x ^ { 6 } - 22$ 
B)  $6 \times 13$ 
C)  $- 6 x ^ { 7 } + 25 x ^ { 6 } + 4$ 
D)  $- 6 x ^ { 7 } + 34 x ^ { 6 } + 4$

Question 20

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
-$$\left( 10 a ^ { n } - b ^ { n } \right) ^ { 2 }$$

Accepted Answer

A)  $100 a ^ { n } - 20 a ^ { n } b ^ { n } + b ^ { n }$ 
B)  $100 a ^ { 2 n } - 20 a b + b ^ { 2 n }$ 
C)  $100 a ^ { 2 n } - 20 a ^ { n } b ^ { n } + b ^ { 2 n }$ 
D)  $100 a ^ { 2 n } - 10 a ^ { n } b ^ { n } + b ^ { 2 n }$ 
A)  $100 a ^ { n } - 20 a ^ { n } b ^ { n } + b ^ { n }$ 
B)  $100 a ^ { 2 n } - 20 a b + b ^ { 2 n }$ 
C)  $100 a ^ { 2 n } - 20 a ^ { n } b ^ { n } + b ^ { 2 n }$ 
D)  $100 a ^ { 2 n } - 10 a ^ { n } b ^ { n } + b ^ { 2 n }$

Find the product. Assume all variable exponents represent whole numbers. - $\left( x ^ { 2 } + x + 3 \right) \left( x ^ { 2 } + x + 6 \right)$

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - $\left( y ^ { 3 } - 7 \right) \left( y ^ { 3 } + 7 \right)$

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - $[ ( 3 x - 4 ) + 2 y ] ^ { 2 }$

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - $12 x ^ { 9 } y ^ { 8 } + 54 x ^ { 2 } y ^ { 6 } + 54 x ^ { 6 } y ^ { 4 }$

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - $\left( a ^ { n } + 3 b ^ { n } \right) ^ { 2 }$

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - $\left( 11 x y ^ { 2 } - x y \right) ^ { 2 }$

Give the requested components for the polynomial. - $x ^ { 5 } - 2 x ^ { 4 } y ^ { 8 } + 11 x y - 7 x + 9$ ; degree of each term and degree of the polynomial

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - $( 5 x + 3 y ) ^ { 2 }$

Subtract the polynomials. Assume all variable exponents represent whole numbers. - $\left( 2 x ^ { 2 n } - 7 x ^ { n } - 19 \right) - \left( 9 x ^ { 2 n } - 5 x ^ { n } + 13 \right)$

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - $42 x ^ { 3 } y + 54 x y ^ { 6 }$

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - $( x + y + 12 ) ^ { 2 }$

Add the polynomials. Assume all variable exponents represent whole numbers. - $\left( 4 x ^ { 6 } - 8 x ^ { 4 } + 8 x \right) + \left( 5 x ^ { 6 } - 2 x ^ { 4 } + 5 x \right)$

Add the polynomials. Assume all variable exponents represent whole numbers. - $\left( 2 x ^ { 9 } - 6 x ^ { 8 } - 7 x ^ { 7 } - 8 \right) + \left( 4 x ^ { 9 } + 8 x ^ { 8 } + 3 x ^ { 7 } + 4 \right)$

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers. - $( x - 10 y ) ( 4 x - 3 y )$

Give the requested components for the polynomial. - $- 5 x ^ { 3 } + 6 x ^ { 2 } + 4 x$ ; the degree of the polynomial and the leading coefficient of the polynomial.

Solve the problem. -Find the area of the rectangle by multiplying the length and the width of the large rectangle using the FOIL method.

Give the requested components for the polynomial. - $5 x ^ { 8 } y + x ^ { 7 } y ^ { 3 } + 13 y ^ { 2 }$ ; leading term and leading coefficient of the polynomial

Add the polynomials. Assume all variable exponents represent whole numbers. - $\left( 5 x ^ { 2 n } - x ^ { n } - 1 \right) + \left( x ^ { 2 n } + 4 x ^ { n } + 10 \right)$

Add the polynomials. Assume all variable exponents represent whole numbers. - $\left( - 9 x ^ { 7 } + 18 x ^ { 6 } - 13 \right) + \left( 3 x ^ { 7 } + 16 x ^ { 6 } - 9 \right)$

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - $\left( 10 a ^ { n } - b ^ { n } \right) ^ { 2 }$

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Exam 5: Polynomials, Polynomial Functions, and Factoring

Find the product. Assume all variable exponents represent whole numbers. - (x2+x+3)(x2+x+6)\left( x ^ { 2 } + x + 3 \right) \left( x ^ { 2 } + x + 6 \right)(x2+x+3)(x2+x+6)

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - (y3−7)(y3+7)\left( y ^ { 3 } - 7 \right) \left( y ^ { 3 } + 7 \right)(y3−7)(y3+7)

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - [(3x−4)+2y]2[ ( 3 x - 4 ) + 2 y ] ^ { 2 }[(3x−4)+2y]2

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - 12x9y8+54x2y6+54x6y412 x ^ { 9 } y ^ { 8 } + 54 x ^ { 2 } y ^ { 6 } + 54 x ^ { 6 } y ^ { 4 }12x9y8+54x2y6+54x6y4

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - (an+3bn)2\left( a ^ { n } + 3 b ^ { n } \right) ^ { 2 }(an+3bn)2

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - (11xy2−xy)2\left( 11 x y ^ { 2 } - x y \right) ^ { 2 }(11xy2−xy)2

Give the requested components for the polynomial. - x5−2x4y8+11xy−7x+9x ^ { 5 } - 2 x ^ { 4 } y ^ { 8 } + 11 x y - 7 x + 9x5−2x4y8+11xy−7x+9 ; degree of each term and degree of the polynomial

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - (5x+3y)2( 5 x + 3 y ) ^ { 2 }(5x+3y)2

Subtract the polynomials. Assume all variable exponents represent whole numbers. - (2x2n−7xn−19)−(9x2n−5xn+13)\left( 2 x ^ { 2 n } - 7 x ^ { n } - 19 \right) - \left( 9 x ^ { 2 n } - 5 x ^ { n } + 13 \right)(2x2n−7xn−19)−(9x2n−5xn+13)

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - 42x3y+54xy642 x ^ { 3 } y + 54 x y ^ { 6 }42x3y+54xy6

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - (x+y+12)2( x + y + 12 ) ^ { 2 }(x+y+12)2

Add the polynomials. Assume all variable exponents represent whole numbers. - (4x6−8x4+8x)+(5x6−2x4+5x)\left( 4 x ^ { 6 } - 8 x ^ { 4 } + 8 x \right) + \left( 5 x ^ { 6 } - 2 x ^ { 4 } + 5 x \right)(4x6−8x4+8x)+(5x6−2x4+5x)

Add the polynomials. Assume all variable exponents represent whole numbers. - (2x9−6x8−7x7−8)+(4x9+8x8+3x7+4)\left( 2 x ^ { 9 } - 6 x ^ { 8 } - 7 x ^ { 7 } - 8 \right) + \left( 4 x ^ { 9 } + 8 x ^ { 8 } + 3 x ^ { 7 } + 4 \right)(2x9−6x8−7x7−8)+(4x9+8x8+3x7+4)

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers. - (x−10y)(4x−3y)( x - 10 y ) ( 4 x - 3 y )(x−10y)(4x−3y)

Give the requested components for the polynomial. - −5x3+6x2+4x- 5 x ^ { 3 } + 6 x ^ { 2 } + 4 x−5x3+6x2+4x ; the degree of the polynomial and the leading coefficient of the polynomial.