Test Review

GCF & Factor

100

60x + 10

10(6x + 1)

200

12x + 24y

12(x + 2y)

300

8xy - 16x³y + 10y

2y(4x - 8x³ + 5)

400

14x²y - 21xy + 35xy²

7xy(2x - 3 + 5y)

500

56x¹²y⁵z⁹ + 40x⁶y⁷z³b + 72x¹⁰y⁹z³b⁴

8x⁶y⁵z³(7x⁶z⁶ + 5y²b + 9x⁴y⁴b⁴)

Difference of Squares

100

64 - 25x²

(8 + 5w) (8 - 5w)

200

121w² - 225

(11w + 15) (11w - 15)

300

16a² - 81b²

(4a + 9b) (4a - 9b)

400

81w⁴ - 144c²

(9w² + 12c) (9w² - 12c)

500

64x⁶ - 81c⁴

(8x³ + 9c²) (8x³ - 9c²)

Grouping

100

a² - 4ac + ab - 4bc

a(a - 4c) + b(a - 4c)

(a - 4c) (a + b)

200

2x² - 3xz - 2xy + 3yz

x(2x - 3z) - y(2x - 3z)

(2x - 3z) (x - y)

300

24am - 9an + 40bm - 15bn

3a(8m - 3n) + 5b(8m - 3n)

(8m - 3n) (3a + 5b)

400

Which of the following is a factor of the polynomial:

x³ − 5x² + 11x − 55

A. (x + 5)

B. (x − 5)

C. (x + 11)

D. (x − 11)

x²(x - 5) + 11(x - 5)

(x - 5) (x² + 11)

B

500

Factor the following polynomial by using Grouping:

 x³ − 2x² − 16x + 32

F. (x + 4)(x − 4)(x − 2)

G. (x − 4)(x − 4)(x + 2)

H. (x + 4)(x − 4)(x + 2)

J. (x + 16) (x − 2)(x + 2)

x²(x - 2) - 16(x - 2)

(x² - 16) (x - 2)

(x - 4) (x + 4) (x - 2)

F

Trinomials

100

x² - 5x - 6

(x - 6) (x + 1)

200

2a² + 13a - 24

2a² + 16a - 3a - 24

2a(a + 8) - 3(a + 8)

(2a - 3) (a + 8)

300

Which of the following is the factored form of the polynomial: 16w² + 24w + 9 ?

A. (4w + 3)²

B. (4w − 3)²

C. (8w + 3)²

D. (8w − 3)²

16w² + 12w + 12w + 9

4w(4w + 3) +3(4w + 9)

(4w + 3) (4w + 3)

(4w + 3)²

A

400

Factor completely: 12x² − 48x + 48

A. 12 (x − 2)(x − 2)

B. 12 (x + 2)(x + 2)

C. 12 (x − 4)(x − 1)

D. 12 (x + 4)(x − 1)

12(x² -4x + 4)

12(x² - 2x - 2x + 4)

12[x(x - 2) - 2(x - 2)]

12(x - 2) (x - 2)

A

500

Makenzie is working on some artwork that will be framed. The area of the rectangular frame is represented by the polynomial: 

3m² + 5m − 12

Which of the following expressions can be used to represent the length and width of the frame?

A. (3m + 4)(m − 3)

B. (3m − 4)(m + 3)

C. (3m + 3)(m − 4)

D. (3m − 3)(m + 4)

3m² + 9m - 4m - 12

3m(m + 3) - 4(m + 3)

(m + 3) (3m - 4)

B

Who Knows

100

Which expression is a factor of ?

5x² − 30x − 80

Hint: Factor out GCF first!

A. x + 4

B. x + 8

C. x − 4

D. x − 8

5(x² - 6x - 16)

5(x - 8) (x + 2)

x - 8

D

200

Which expression is the factored form of the polynomial: x² + 10x + 24 ?

F. (x + 1)(x + 24)

G. (x + 2)(x + 12)

H. (x + 3)(x + 8)

J. (x + 4)(x + 6)

(x + 6) (x + 4)

J

300

Which expression is the factored form of the polynomial: 9n² − 25 ?

F. (3n − 5)²

G. (3n + 5)(3n − 5)

H. 9 (n − 4)²

J. 9 (n + 4)(n − 4)

(3n + 5) (3n - 5)

G

400

Choose two factors to create an expression equivalent to 4x² - 81

4x² - 81 = (2x + 9) (2x - 9)

500

The area of a rectangle is described by the polynomial:

A (x) = 2x² − 7x − 15

Which pair of expressions could represent the length and width of the rectangle?

A. (2x + 5)(x − 3)

B. (2x − 5)(x + 3)

C. (2x + 3)(x − 5)

D. (2x − 3)(x + 5)

2x² + 3x - 10x - 15

x(2x + 3) - 5(2x + 3)

(2x + 3) (x - 5)

C