Introduction to Factoring

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Show your work for each problem.

1.
Which of the following is a factor of 12?
1. a)4
2. b)5
3. c)9
4. d)7
2.
What is the GCF of 8 and 12?
3.
Factor out the GCF: $4x + 8$
1. a) $2(2x + 4)$
2. b) $4(x + 2)$
3. c) $4(x + 8)$
4. d) $8(x + 1)$
4.
Factor: $3x + 9$
5.
Factor: $x^2 + 4x$ . Write as $x(\text{something})$ . What goes in the parentheses?
6.
Factor: $x^2 + 5x + 6$
1. a) $(x + 2)(x + 3)$
2. b) $(x + 5)(x + 1)$
3. c) $(x - 2)(x - 3)$
4. d) $(x + 1)(x + 6)$
7.
Factor: $x^2 + 8x + 15$
8.
Factor $x^2 + 9x + 20$ in the form $(x + a)(x + b)$ with $a < b$ . What is $b$ ?
9.
Factor out the GCF: $6x^2 + 9x$
1. a) $3x(2x + 3)$
2. b) $6x(x + 9)$
3. c) $3(2x^2 + 3x)$
4. d) $x(6x + 9)$
10.
Factor: $x^2 + 6x + 8$
11.
Factor: $x^2 - 5x + 6$
1. a) $(x - 1)(x - 6)$
2. b) $(x - 2)(x - 3)$
3. c) $(x + 2)(x + 3)$
4. d) $(x + 2)(x - 3)$
12.
Factor: $x^2 + x - 12$
13.
Factor completely: $2x^2 + 10x + 12$ . The result has the form $a(x + b)(x + c)$ with $b < c$ . What is $c$ ?
14.
Factor: $x^2 - 4x - 21$
15.
Which expression is completely factored?
1. a) $3(x+2)(x+4)$
2. b) $3x(x + 6) + 24$
3. c) $3(x^2 + 6x + 8)$
4. d) $(3x+6)(x+4)$
16.
Factor out the GCF: $5x^2 - 15x = \square\,(x - 3)$ . What goes in the box?
17.
Find all factor pairs of 18.