Topic 6 - Polynomials and Factoring

Adding and Substracting Polynomials

100

Combine like terms 

−2x² + x + 5x³ + 4x + 2x²

What is

5x³ + 5x

200

Simplify

(3x³ + 2x² + 4x) + (4x³ + 6x² − 3x).

A.   7x³ + 8x² + x

B.   7x³ + 4x² + x

C.   7x³ + 8x² − x

D.   7x³ + 4x² − x

What is 

A. 7x³ + 8x² + x

300

Simplify (5x² + 4x − 7) − (x² − 2x).

A.   4x² + 6x

B.   4x² + 6x − 7

C.   4x² − 2x − 7

D.   4x² − 2x + 7

What is 

B.   4x² + 6x − 7

400

Simplify
(3x³ + 7x − 1) + (4x³ − 9x² − 11x).

What is

7x³ - 9x² - 4x -1

500

Simplify (−5x + 7) − (x² − 3x + 2).

A.   −6x² + 3x + 9

B.   −6x² + 3x + 5

C.   −x² + 2x + 5

D.   −x² − 8x + 5

What is 

C.   −x² + 2x + 5

Multiplying and Dividing Polynomials

100

Find the product.
(2y − 6)²

A.   4y² − 24y + 36

B.   4y² + 24y − 36

C.   4y² + 36

D.   4y² − 16y − 12

What is

A.   4y² − 24y + 36

200

What is the product of
(4x² + 6)(x² − 3x + 8)?

A    4x⁴ − 12x³ + 38x² − 3x + 48

B    4x⁴ − 12x³ + 38x² − 18x + 48

C    4x⁴ − 12x³ + 38x² − 3x + 5

D    4x⁴ − 12x³ + 38x² − 18x + 14

What is 

B    4x⁴ − 12x³ + 38x² − 18x + 48

300

Solve 

24x³ − 16x² + 20x divided by 4x?

What is

6x² - 4x + 5

400

The product of −7y²(−2y⁴ + y² − 1) is

A.  14y⁸ − 7y⁴ − 7y

B.  14y⁶ − 7y⁴ + 7y²

C.  −14y⁶ + 7y⁴ − 7y²

D.  −9y⁶ − 6y⁴ − 8y²

What is

B.  14y⁶ − 7y⁴ + 7y²

500

Show the quotient of  

56x⁶ - 14x⁴ - 42x³ divided by 7x²

What is

8x⁴ - 2x² - 6x

Factoring Polynomials

100

What is the GCF of 

x³ + x² + x

What is 

x

200

What is the GCF of 

-64x³ + 48x² - 32x

What is

16x

300

Factor out the GCF from the terms of the polynomial 

−2x⁵ − 6x³ − 16x².

A.  −2x(x⁴ + 3x² + 8x)

B.  −2x²(x³ + 3x + 8)

C.  −2x²(−x³ − 3x − 8)

D.  The polynomial is already fully factored.

What is

B.  −2x²(x³ + 3x + 8)

400

Factor out the GCF from the terms of the polynomial 

12x⁴ − 16x³ + 8x² − 28x

What is

4x(3x³ - 4x² + 2x -7)

500

Factor out the GCF from the terms of the polynomial

−15y⁴ + 12y² − 9y

What is

-3y(5y³ - 4y + 3)

Factoring Trinomials

100

Complete the expressions to write the factored form of 

y² + 11y + 28

What is

(y + 4) (y + 7)

200

Find the factored form of
x² − 9x + 20.

A    (x − 4)(x + 5)

B    (x + 4)(x + 5)

C    (x − 4)(x − 5)

D    cannot be determined

What is

C    (x − 4)(x − 5)

300

What is the factored form of y² + 6y − 16?

A   (y − 4)(y − 4)

B   (y − 8)(y + 2)

C   (y + 8)(y − 2)

D   (y + 4)(y − 4)

What is 

C   (y + 8)(y − 2)

400

What is the factored form of x² + 4xy − 21y²?

A   xy(x + 4 − 21y)

B   (x − 3y)(x + 7y)

C   x(x + 4y) + y(4x − 21y)

D   (x + 3y)(x − 7y)

What is

B   (x − 3y)(x + 7y)

500

Simply and factor

x² − 17x + 52

What is

(x - 13) (x - 4)

Mixed Review

100

What is the GCF of 70 and 42?

GCF =

What is

7

200

What is the solution to the equation 

–45 − x = 4(x + 10)?

x =

What is

x = -17

300

Choose the list that includes ALL the common factors of 36 and 24.

A   2, 3, 4, 6, 9, 12, 18

B   1, 2, 3, 4, 6, 12

C   1, 2, 3, 4, 5, 8, 9, 12, 18, 36

D   1, 2, 3, 4, 6, 8, 12, 24

What is

B   1, 2, 3, 4, 6, 12

400

Evaluate the expression for 

y = 2 

3y² − 7y + y³

What is

6

500

Maria is renting kayaks from a local shop that charges a $7 fee, plus an hourly rate of $5.50. For how long can Maria rent the kayak if she pays a total of $40?

A   5 hours

B   6 hours

C   7 hours

D   8 hours

What is 

B   6 hours