## Algebra: A Combined Approach (4th Edition)

Chapter 6 - Section 6.2 - Exercise Set: 93 (Answer) $x^{2n} + 8x^n - 20$ = $(x^n + 10)(x^n - 2)$
Chapter 6 - Section 6.2 - Exercise Set: 93 (Solution) Factorize : $x^{2n} + 8x^n - 20$ First, take $(x^{2n} + 8x^n - 20)$ to be $(x^n + \triangle)(x^n + \square)$ For this, we have to look for two numbers whose product is -20 and whose sum is +8. Factors of -20 $\Longleftrightarrow$ Sum of Factors 1,-20 $\Longleftrightarrow$ -19 (Incorrect sum) 2,-10 $\Longleftrightarrow$ -8 (Incorrect sum) 4,-5 $\Longleftrightarrow$ -1 (Incorrect sum) 5,-4 $\Longleftrightarrow$ 1 (Incorrect sum) 10,-2 $\Longleftrightarrow$ 8 (Correct sum, the two numbers are 10 and -2) 20,-1 $\Longleftrightarrow$ 19 (Incorrect sum) Thus, $x^{2n} + 8x^n - 20$ = $(x^n + 10)(x^n - 2)$