Question 1

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
-$$28 x ^ { 5 } - 8 x ^ { 2 }$$

Accepted Answer

A)  $x ^ { 2 } \left( 28 x ^ { 3 } - 8 \right)$ 
B)  $4 x ^ { 2 } \left( 7 x ^ { 4 } - 2 \right)$ 
C)  $4 x ^ { 2 } \left( 7 x ^ { 3 } - 2 \right)$ 
D)  $4 \left( 7 x ^ { 5 } - 2 x ^ { 2 } \right)$

Question 2

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
-$$6 x ^ { 9 } + 4 x ^ { 4 } - 10 x ^ { 2 }$$

Accepted Answer

A)  $2 \left( 3 x ^ { 9 } + 2 x ^ { 4 } - 5 x ^ { 2 } \right)$ 
B)  $2 x ^ { 2 } \left( 3 x ^ { 7 } + 2 x ^ { 2 } - 5 \right)$ 
C)  $x ^ { 2 } \left( 6 x ^ { 7 } + 4 x ^ { 2 } - 10 \right)$ 
D)  No common factor

Question 3

Add the polynomials. Assume all variable exponents represent whole numbers.
-$$\left( 12 x ^ { 2 } y - 10 x y + 11 \right) + \left( - 11 x ^ { 2 } y + 4 x y - 6 \right)$$

Accepted Answer

A)  $x ^ { 2 } y - 6 x y + 5$ 
B)  $23 x ^ { 2 } y + 14 x y + 17$ 
C)  $- x ^ { 2 } y - 14 x y + 17$ 
D)  $- 6 x ^ { 3 } y ^ { 2 } + 5$

Question 4

Subtract the polynomials. Assume all variable exponents represent whole numbers.
-$$\left( 5 x ^ { 4 } y ^ { 2 } + 7 x ^ { 3 } y + 6 y \right) - \left( 3 x ^ { 4 } y ^ { 2 } + 10 x ^ { 3 } y + 11 y + 9 x \right)$$

Accepted Answer

A)  $2 x ^ { 4 } y ^ { 2 } - 3 x ^ { 3 } y - 5 y + 9 x$ 
B)  $8 x ^ { 4 } y ^ { 2 } + 17 x ^ { 3 } y + 17 y + 9 x$ 
C)  $2 x ^ { 4 } y ^ { 2 } + 3 x ^ { 3 } y - 5 y - 9 x$ 
D)  $2 x ^ { 4 } y ^ { 2 } - 3 x ^ { 3 } y - 5 y - 9 x$

Question 5

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
-$$\left( 3 x ^ { 3 } - 6 \right) \left( x ^ { 2 } - 5 \right)$$

Accepted Answer

A)  $3 x ^ { 5 } - 21 x ^ { 3 } + 30$ 
B)  $3 x ^ { 5 } - 15 x ^ { 3 } - 6 x ^ { 2 } - 30$ 
C)  $3 x ^ { 5 } - 15 x ^ { 3 } - 6 x ^ { 2 } + 30$ 
D)  $4 x ^ { 5 } - 8 x ^ { 3 } - 7 x ^ { 2 } + 11$

Question 6

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
-$$f ( x ) = 2 x ^ { 2 } - 3 x - 2$$

Accepted Answer

A)  rises to the left and falls to the right
 
B)  falls to the left and falls to the right
 
C)  falls to the left and rises to the right
 
D)  rises to the left and rises to the right

Question 7

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
-$28 x ^ { 2 n } - 20 x ^ { n }$

Accepted Answer

A)  $4 x ^ { n } \left( 7 x ^ { n } - 5 x \right)$ 
B)  $4 x ^ { 2 n } \left( 7 x ^ { n } - 5 \right)$ 
C)  $4 x ^ { 2 } \left( 7 x ^ { n } - 5 \right)$ 
D)  $4 x ^ { n } \left( 7 x ^ { n } - 5 \right)$

Question 8

Give the requested components for the polynomial.
-$7 x ^ { 8 } - 12 x ^ { 5 } y ^ { 5 } - x y ^ { 2 } + 3$; the leading term and the coefficient of each term

Accepted Answer

A)  leading term: 10; coefficients: $8,10,3$, and 0 
B)  leading term: $7 x ^ { 8 }$; coefficients: $7,12,1$, and 3 
C)  leading term: 8 ; coefficients: 8,5 , and 1 
D)  leading term: $- 12 x ^ { 5 } y ^ { 5 }$; coefficients: $7 , - 12 , - 1$, and 3

Question 9

Subtract the polynomials. Assume all variable exponents represent whole numbers.
-$$\left( 4 x ^ { 5 } + 5 x ^ { 4 } - 6 x ^ { 3 } - 9 \right) - \left( 6 x ^ { 5 } + 9 x ^ { 4 } + 9 x ^ { 3 } - 6 \right)$$

Accepted Answer

A)  $10 x ^ { 5 } + 14 x ^ { 4 } + 3 x ^ { 3 } - 15$ 
B)  $- 2 x ^ { 5 } - 4 x ^ { 4 } - 15 x ^ { 3 } - 3$ 
C)  $10 x ^ { 5 } + 14 x ^ { 4 } + 3 x ^ { 3 } - 3$ 
D)  $- 2 x ^ { 5 } + 14 x ^ { 4 } + 3 x ^ { 3 } - 15$

Question 10

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers.
-$$[ ( 2 x - 1 ) + 3 y ] [ ( 2 x - 1 ) - 3 y ]$$

Accepted Answer

A)  $4 x ^ { 2 } - 4 x + 1 + 12 x y - 6 y + 9 y ^ { 2 }$ 
B)  $4 x ^ { 2 } + 4 x + 1 - 9 y ^ { 2 }$ 
C)  $4 x ^ { 2 } - 4 x + 1 - 9 y ^ { 2 }$ 
D)  $4 x ^ { 2 } - 4 x + 1 + 9 y ^ { 2 }$

Question 11

Subtract the polynomials. Assume all variable exponents represent whole numbers.
-$\left( 10 x ^ { 8 } + 4 x ^ { 7 } - 11 x ^ { 2 } + 9 \right) - \left( 6 x ^ { 8 } - 6 x ^ { 5 } + 5 x ^ { 2 } - 3 \right)$

Accepted Answer

A)  $4 x ^ { 8 } + 4 x ^ { 7 } + 6 x ^ { 5 } - 16 x ^ { 2 } + 12$ 
B)  $- 4 x ^ { 8 } + 4 x ^ { 7 } - 6 x ^ { 5 } - 16 x ^ { 2 } + 12$ 
C)  $4 x ^ { 8 } + 4 x ^ { 7 } - 6 x ^ { 5 } - 16 x ^ { 2 } + 12$ 
D)  $- 4 x ^ { 8 } + 4 x ^ { 7 } + 6 x ^ { 5 } - 16 x ^ { 2 } + 12$

Question 12

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

Accepted Answer

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

Question 13

Add the polynomials. Assume all variable exponents represent whole numbers.
-$$\left( \frac { 3 } { 5 } x ^ { 2 } + \frac { 3 } { 4 } x - \frac { 4 } { 5 } \right) + \left( \frac { 3 } { 4 } x ^ { 2 } - \frac { 2 } { 5 } x - \frac { 1 } { 4 } \right)$$

Accepted Answer

A)  $\frac { 27 } { 20 } x ^ { 2 } + \frac { 7 } { 20 } x - \frac { 21 } { 20 }$ 
B)  $\frac { 27 } { 20 } x ^ { 4 } + \frac { 7 } { 20 } x ^ { 2 } - \frac { 21 } { 20 }$ 
C)  $\frac { 9 } { 2 } x ^ { 2 } - 3 x + 2$ 
D)  $\frac { 17 } { 10 } x ^ { 6 } - \frac { 21 } { 20 }$

Question 14

Evaluate the polynomial function.
-If $f ( x ) = x ^ { 2 } + 5 x + 3$, find $f ( a + h ) - f ( a )$.

Accepted Answer

A)  $2 a h + h ^ { 2 } + 5 a + 5 h$ 
B)  $a ^ { 2 } + 2 a h + h ^ { 2 } + 5 a + 5 h + 3$ 
C)  $2 a h + h ^ { 2 } + 5 a + 6$ 
D)  $2 a h + h ^ { 2 } + 5 a$

Question 15

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
-$$f ( x ) = - 3 x ^ { 2 } - 2 x + 2$$

Accepted Answer

A)  rises to the left and rises to the right
 
B)  rises to the left and falls to the right
 
C)  falls to the left and falls to the right
 
D)  falls to the left and rises to the right

Question 16

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers.
-$$\left( 4 x y ^ { 2 } + 10 x \right) \left( 4 x y ^ { 2 } - 10 x \right)$$

Accepted Answer

A)  $8 x ^ { 2 } y ^ { 4 } - 80 x ^ { 2 } y ^ { 4 } - 20 x ^ { 2 }$ 
B)  $16 x ^ { 2 } y ^ { 4 } - 100 x ^ { 2 }$ 
C)  $8 x ^ { 2 } y ^ { 4 } - 20 x ^ { 2 }$ 
D)  $16 x ^ { 2 } y ^ { 4 } - 80 x ^ { 2 } y ^ { 4 } - 100 x ^ { 2 }$

Question 17

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
-$15 x y + 21 x z - 6 x w$

Accepted Answer

A)  $3 ( 5 x y + 7 x z - 2 x w )$ 
B)  $x ( 15 y + 21 z - 6 w )$ 
C)  $3 x ( 5 y + 7 z - 2 w )$ 
D)  $x ( 15 x y + 21 x z - 6 x w )$

Question 18

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers.
-$$( 6 x + 11 ) ( 6 x - 11 )$$

Accepted Answer

A)  $x ^ { 2 } - 121$ 
B)  $36 x ^ { 2 } - 132 x - 121$ 
C)  $36 x ^ { 2 } + 132 x - 121$ 
D)  $36 \mathrm { x } ^ { 2 } - 121$

Question 19

Multiply the monomials. Assume any variable exponents represent whole numbers.
-$$\left( 12 x ^ { 5 } y ^ { 7 } z \right) \left( - 9 x ^ { 2 } y z ^ { 3 } \right)$$

Accepted Answer

A)  $3 x ^ { 10 } y ^ { 7 } z ^ { 3 }$ 
B)  $- 108 x ^ { 10 } y ^ { 7 } z ^ { 3 }$ 
C)  $- 108 x ^ { 7 } y ^ { 8 } z ^ { 4 }$ 
D)  $3 x ^ { 7 } y ^ { 8 } z ^ { 4 }$

Question 20

Subtract the polynomials. Assume all variable exponents represent whole numbers.
-$$\left( 4 y ^ { 2 n } + 4 y ^ { n } - 1 \right) - \left( 5 y ^ { 2 n } + 6 y ^ { n } + 4 \right)$$

Accepted Answer

A)  $y ^ { 2 n } - 2 y ^ { n } - 5$ 
B)  $- y ^ { 2 n } - 2 y ^ { n } - 5$ 
C)  $- y ^ { 2 n } - 2 y ^ { n } + 3$ 
D)  $- y ^ { 2 n } + 2 y ^ { n } - 5$

Exam 5: Polynomials, Polynomial Functions, and Factoring

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - $28 x ^ { 5 } - 8 x ^ { 2 }$

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - $6 x ^ { 9 } + 4 x ^ { 4 } - 10 x ^ { 2 }$

Add the polynomials. Assume all variable exponents represent whole numbers. - $\left( 12 x ^ { 2 } y - 10 x y + 11 \right) + \left( - 11 x ^ { 2 } y + 4 x y - 6 \right)$

Subtract the polynomials. Assume all variable exponents represent whole numbers. - $\left( 5 x ^ { 4 } y ^ { 2 } + 7 x ^ { 3 } y + 6 y \right) - \left( 3 x ^ { 4 } y ^ { 2 } + 10 x ^ { 3 } y + 11 y + 9 x \right)$

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers. - $\left( 3 x ^ { 3 } - 6 \right) \left( x ^ { 2 } - 5 \right)$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - $f ( x ) = 2 x ^ { 2 } - 3 x - 2$

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - $28 x ^ { 2 n } - 20 x ^ { n }$

Give the requested components for the polynomial. - $7 x ^ { 8 } - 12 x ^ { 5 } y ^ { 5 } - x y ^ { 2 } + 3$ ; the leading term and the coefficient of each term

Subtract the polynomials. Assume all variable exponents represent whole numbers. - $\left( 4 x ^ { 5 } + 5 x ^ { 4 } - 6 x ^ { 3 } - 9 \right) - \left( 6 x ^ { 5 } + 9 x ^ { 4 } + 9 x ^ { 3 } - 6 \right)$

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - $[ ( 2 x - 1 ) + 3 y ] [ ( 2 x - 1 ) - 3 y ]$

Subtract the polynomials. Assume all variable exponents represent whole numbers. - $\left( 10 x ^ { 8 } + 4 x ^ { 7 } - 11 x ^ { 2 } + 9 \right) - \left( 6 x ^ { 8 } - 6 x ^ { 5 } + 5 x ^ { 2 } - 3 \right)$

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

Add the polynomials. Assume all variable exponents represent whole numbers. - $\left( \frac { 3 } { 5 } x ^ { 2 } + \frac { 3 } { 4 } x - \frac { 4 } { 5 } \right) + \left( \frac { 3 } { 4 } x ^ { 2 } - \frac { 2 } { 5 } x - \frac { 1 } { 4 } \right)$

Evaluate the polynomial function. -If $f ( x ) = x ^ { 2 } + 5 x + 3$ , find $f ( a + h ) - f ( a )$ .

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - $f ( x ) = - 3 x ^ { 2 } - 2 x + 2$

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - $\left( 4 x y ^ { 2 } + 10 x \right) \left( 4 x y ^ { 2 } - 10 x \right)$

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - $15 x y + 21 x z - 6 x w$

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - $( 6 x + 11 ) ( 6 x - 11 )$

Multiply the monomials. Assume any variable exponents represent whole numbers. - $\left( 12 x ^ { 5 } y ^ { 7 } z \right) \left( - 9 x ^ { 2 } y z ^ { 3 } \right)$

Subtract the polynomials. Assume all variable exponents represent whole numbers. - $\left( 4 y ^ { 2 n } + 4 y ^ { n } - 1 \right) - \left( 5 y ^ { 2 n } + 6 y ^ { n } + 4 \right)$

Exam 5: Polynomials, Polynomial Functions, and Factoring

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - 28x5−8x228 x ^ { 5 } - 8 x ^ { 2 }28x5−8x2

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - 6x9+4x4−10x26 x ^ { 9 } + 4 x ^ { 4 } - 10 x ^ { 2 }6x9+4x4−10x2

Add the polynomials. Assume all variable exponents represent whole numbers. - (12x2y−10xy+11) +(−11x2y+4xy−6) \left( 12 x ^ { 2 } y - 10 x y + 11 \right) + \left( - 11 x ^ { 2 } y + 4 x y - 6 \right) (12x2y−10xy+11) +(−11x2y+4xy−6)

Subtract the polynomials. Assume all variable exponents represent whole numbers. - (5x4y2+7x3y+6y) −(3x4y2+10x3y+11y+9x) \left( 5 x ^ { 4 } y ^ { 2 } + 7 x ^ { 3 } y + 6 y \right) - \left( 3 x ^ { 4 } y ^ { 2 } + 10 x ^ { 3 } y + 11 y + 9 x \right) (5x4y2+7x3y+6y) −(3x4y2+10x3y+11y+9x)

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers. - (3x3−6) (x2−5) \left( 3 x ^ { 3 } - 6 \right) \left( x ^ { 2 } - 5 \right) (3x3−6) (x2−5)

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - f(x) =2x2−3x−2f ( x ) = 2 x ^ { 2 } - 3 x - 2f(x) =2x2−3x−2

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - 28x2n−20xn28 x ^ { 2 n } - 20 x ^ { n }28x2n−20xn

Give the requested components for the polynomial. - 7x8−12x5y5−xy2+37 x ^ { 8 } - 12 x ^ { 5 } y ^ { 5 } - x y ^ { 2 } + 37x8−12x5y5−xy2+3 ; the leading term and the coefficient of each term

Subtract the polynomials. Assume all variable exponents represent whole numbers. - (4x5+5x4−6x3−9) −(6x5+9x4+9x3−6) \left( 4 x ^ { 5 } + 5 x ^ { 4 } - 6 x ^ { 3 } - 9 \right) - \left( 6 x ^ { 5 } + 9 x ^ { 4 } + 9 x ^ { 3 } - 6 \right) (4x5+5x4−6x3−9) −(6x5+9x4+9x3−6)

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - [(2x−1) +3y][(2x−1) −3y][ ( 2 x - 1 ) + 3 y ] [ ( 2 x - 1 ) - 3 y ][(2x−1) +3y][(2x−1) −3y]

Subtract the polynomials. Assume all variable exponents represent whole numbers. - (10x8+4x7−11x2+9) −(6x8−6x5+5x2−3) \left( 10 x ^ { 8 } + 4 x ^ { 7 } - 11 x ^ { 2 } + 9 \right) - \left( 6 x ^ { 8 } - 6 x ^ { 5 } + 5 x ^ { 2 } - 3 \right) (10x8+4x7−11x2+9) −(6x8−6x5+5x2−3)

Add the polynomials. Assume all variable exponents represent whole numbers. - (−4x2y−xy) +(8x2y+7xy) \left( - 4 x ^ { 2 } y - x y \right) + \left( 8 x ^ { 2 } y + 7 x y \right) (−4x2y−xy) +(8x2y+7xy)

Evaluate the polynomial function. -If f(x) =x2+5x+3f ( x ) = x ^ { 2 } + 5 x + 3f(x) =x2+5x+3 , find f(a+h) −f(a) f ( a + h ) - f ( a ) f(a+h) −f(a) .

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - f(x) =−3x2−2x+2f ( x ) = - 3 x ^ { 2 } - 2 x + 2f(x) =−3x2−2x+2

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - (4xy2+10x) (4xy2−10x) \left( 4 x y ^ { 2 } + 10 x \right) \left( 4 x y ^ { 2 } - 10 x \right) (4xy2+10x) (4xy2−10x)

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - 15xy+21xz−6xw15 x y + 21 x z - 6 x w15xy+21xz−6xw

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - (6x+11) (6x−11) ( 6 x + 11 ) ( 6 x - 11 ) (6x+11) (6x−11)

Multiply the monomials. Assume any variable exponents represent whole numbers. - (12x5y7z) (−9x2yz3) \left( 12 x ^ { 5 } y ^ { 7 } z \right) \left( - 9 x ^ { 2 } y z ^ { 3 } \right) (12x5y7z) (−9x2yz3)

Subtract the polynomials. Assume all variable exponents represent whole numbers. - (4y2n+4yn−1) −(5y2n+6yn+4) \left( 4 y ^ { 2 n } + 4 y ^ { n } - 1 \right) - \left( 5 y ^ { 2 n } + 6 y ^ { n } + 4 \right) (4y2n+4yn−1) −(5y2n+6yn+4)