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: 2

Answer

Practice 2a (Answer) $x^{2} - 23x + 22$ $=(x - 1)(x - 22)$ Practice 2b (Answer) $x^{2} - 27x + 50$ $= (x - 2)(x - 25)$

Work Step by Step

Practice 2a (Solution) Factor : $x^{2} - 23x + 22$ To begin by writing the first terms of the binomial factors (x + $\triangle$)(x + $\square$) Next, to look for two numbers whose product is +22 and whose sum is -23. As the two numbers must have a positive product and a negative sum, pairs of negative factors of 22 are to be investigated only. Factors of 22 $\Longleftrightarrow$ Sum of Factors -1,-22 $\Longleftrightarrow$ -23 (Correct sum, so the numbers are -1 and -22) -2,-11 $\Longleftrightarrow$ -13 Thus, $x^{2} - 23x + 22 = (x - 1)(x - 22)$ Practice 2b (Solution) Factor : $x^{2} - 27x + 50$ To begin by writing the first terms of the binomial factors (x + $\triangle$)(x + $\square$) Next, to look for two numbers whose product is +50 and whose sum is -27. As the two numbers must have a positive product and a negative sum, pairs of negative factors of 50 are to be investigated only. Factors of 50 $\Longleftrightarrow$ Sum of Factors -1,-50 $\Longleftrightarrow$ -51 -2,-25 $\Longleftrightarrow$ -27 (Correct sum, so the numbers are -2 and -25) -5,-10 $\Longleftrightarrow$ -15 Thus, $x^{2} - 27x + 50 = (x - 2)(x - 25)$
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