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# Factoring Expressions Practice Questions (page 2)

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Updated on Oct 3, 2011

#### Practice 2

1. The greatest common factor of 18 and 45 is 9. The variables g and h are common to both terms. The smallest exponent of g is 2 and the smallest exponent of h is 2, so 9g2h2 can be factored out of each term.

18g8h2 ÷ 9g2h2 = 2g6, and 45g2h8 ÷ 9g2h2 = 5h

18g8h2 – 45g2h8 = 9g2h2(2g6 – 5h6)

2. The greatest common factor of 36 and 12 is 12. The variable y is common to both terms, but the variable x is not. The smallest exponent of y is 2, so 12y2 can be factored out of each term.

–36x7y3 ÷ 12y2 = –3x7y, and 12y2 ÷ 12y2 = 1

–36x7y3 + 12y2 = 12y2(–3x7y + 1)

3. The coefficients, 5 and 11, are both prime. No constant can be factored out of the expression. The variables a, b, and c are common to both terms. The smallest exponent of a is 6, the smallest exponent of b is 1, and the smallest exponent of c is 3: a6bc3 can be factored out of each term.

5a9bc3 ÷ a6b5c5 = 5a3, and 11a6b5c5 ÷ a6bc3 = 11b4c2

5a9bc3 – 11a6b5c5 = a6bc3(5a3 – 11b4c2)

4. The greatest common factor of 16, 48, and 28 is 4. The variables j, k, and l are common to each term. The smallest exponent of j is 7, the smallest exponent of k is 3, and the smallest exponent of l is 2: 4j7k3l2 can be factored out of each term.

16j11k3l2 ÷ 4j7k3l2 = 4j4, 48j7k10l4 ÷ 4j7k3l2 = 12k7l2, and 28j9k6l6 ÷ 4j7k3l2 = 7j2k3l4

16j11k3l2 + 48j7k10l4 – 28j9k6l6 = 4j7k3l2(4j4 + 12k7l2 – 7j2k3l4)

5. The greatest common factor of 50, 35, and 45 is 5. The variable t is common to each term, but the variables r and s are not in every term. The exponent of t is 4 in every term, so 5t4 can be factored out of every term.

50r5t4 ÷ 5t4 = 10r5, 35s5t4 ÷ 5t4 = 7s5, and 45r5s5t4 ÷ 5t4 = 9r5s5.

50r5t4 + 35s5t4 + 45r5s5t4 = 5t4(10r5 + 7s5 + 9r5s5)

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