Algebra: A Combined Approach (4th Edition)

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)
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)