GCF & Factor
60x + 10
10(6x + 1)
64 - 25x2
(8 + 5w) (8 - 5w)
a2 - 4ac + ab - 4bc
a(a - 4c) + b(a - 4c)
(a - 4c) (a + b)
x2 - 5x - 6
(x - 6) (x + 1)
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
12x + 24y
12(x + 2y)
121w2 - 225
(11w + 15) (11w - 15)
2x2 - 3xz - 2xy + 3yz
x(2x - 3z) - y(2x - 3z)
(2x - 3z) (x - y)
2a2 + 13a - 24
2a2 + 16a - 3a - 24
2a(a + 8) - 3(a + 8)
(2a - 3) (a + 8)
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)
J
8xy - 16x3y + 10y
2y(4x - 8x3 + 5)
16a2 - 81b2
(4a + 9b) (4a - 9b)
24am - 9an + 40bm - 15bn
3a(8m - 3n) + 5b(8m - 3n)
(8m - 3n) (3a + 5b)
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
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
14x2y - 21xy + 35xy2
7xy(2x - 3 + 5y)
81w4 - 144c2
(9w2 + 12c) (9w2 - 12c)
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
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
Choose two factors to create an expression equivalent to 4x2 - 81
4x2 - 81 = (2x + 9) (2x - 9)
56x12y5z9 + 40x6y7z3b + 72x10y9z3b4
8x6y5z3(7x6z6 + 5y2b + 9x4y4b4)
64x6 - 81c4
(8x3 + 9c2) (8x3 - 9c2)
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
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
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