1. Find the GCF of the product. (3b + 6)(2b – 10)
A) 6 B) 5 C) 2 D) 3
2. Factor completely. b2 – ab – 6a2
A) (b + 3a)(b – 2a) B) (b + 6a)(b – a) C) (b – 3a)(b + 2a) D) (b – 6a)(b + a)
3. Factor completely. 12x3 – 3xy2
A) 3x(2x + y)(2x – y) C) 3x(4x – y)(x + y)
B) 3x(2x – y)2 D) 12x(x – 3y)(x – y)
4. Use the ac test to determine if the following trinomial can be factored.
x2 + 2x + 3
A) Not factorable B) Factorable
5. Factor completely. 25x2 + 30xy + 9y2
A) (25x + 3y)(x + 3y) C) (5x – 3y)(5x + 3y)
B) (5x + y)(5x + 9y) D) (5x + 3y)2
6. Factor. 50x3 – 90x2
A) 50x2(x – 90) B) –10x2(–5x – 90) C) –50x(x2 – 90x) D) –10x2(–5x + 9)
7. State which method should be applied as the first step for factoring the polynomial.
(x – 6y)2 – 1
A) Group the terms. C) Find the GCF.
B) Use the ac method (or trial and error). D) Factor the difference of squares.
8. Factor. 8m4n – 16mn4
A) 8m4n4(m – 2n) B) 8mn(m3 – 2n3) C) 8m4n(1 – 2n3) D) 8m4n(1 – 16mn4)
9. Factor. 3a2(a – b) – 6a(a – b) + 21(a – b)
A) (3a – b)(a2 – 2a + 7) C) (a – b)(3a2 – 6a + 21)
B) 3(a – b)(a2 – 6a + 21) D) 3(a – b)(a2 – 2a + 7)
10. Factor completely. x2 + 3x – 28
A) (x – 4)(x – 7) B) (x – 4)(x + 7) C) (x + 4)(x – 7) D) (x + 1)(x – 28)
11. Factor completely. y3 – 12y2 + 36y
A) y(y – 9)(y + 4) B) y(y + 6)2 C) y(y + 12)(y – 3) D) y(y – 6)2
12. State which method should be applied as the first step for factoring the polynomial.
2a2 + 9a + 10
A) Factor the difference of squares. C) Use the ac method (or trial and error).
B) Find the GCF. D) Group the terms.
13. Factor completely. 6x2 – xy – 5y2
A) (3x – 5y)(2x + y) C) (6x – 5y)(x + y)
B) (6x + 5y)(x – y) D) (3x + 5y)(2x – y)
14. Solve. x2 = –6x
A) 2, 6 B) 6, –6 C) 0, –6 D) 0, 6
15. Factor completely. 5a2 – 125
A) (5a – 1)(a – 125) B) 5a(a – 25) C) 5(a + 5)(a – 5) D) 5(a – 5)2