Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 6 - Section 6.2 - Factoring Trinomials of the Form x2+bx+c - Practice: 1

Answer

Factor : $x^{2}$ + 12x + 20 To begin by writing the first terms of the binomial factors (x + $\triangle$)(x + $\square$) Next, to look for two numbers whose product is +20 and whose sum is +12. As the two numbers must have a positive product and a positive sum, pairs of positive factors of 20 are to be investigated only. Factors of 20 $\Longleftrightarrow$ Sum of Factors 1,20 $\Longleftrightarrow$ 21 2,10 $\Longleftrightarrow$ 12 (Correct sum) 4,5 $\Longleftrightarrow$ 9 Thus, $x^{2}$ + 12x + 20 = (x + 2)(x + 10)

Work Step by Step

Factor : $x^{2}$ + 12x + 20 To begin by writing the first terms of the binomial factors (x + $\triangle$)(x + $\square$) Next, to look for two numbers whose product is +20 and whose sum is +12. As the two numbers must have a positive product and a positive sum, pairs of positive factors of 20 are to be investigated only. Factors of 20 $\Longleftrightarrow$ Sum of Factors 1,20 $\Longleftrightarrow$ 21 2,10 $\Longleftrightarrow$ 12 (Correct sum) 4,5 $\Longleftrightarrow$ 9 Thus, $x^{2}$ + 12x + 20 = (x + 2)(x + 10)
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