Answer
Chapter 6 - Section 6.2 - Exercise Set: 93 (Answer)
$x^{2n} + 8x^n - 20$ = $(x^n + 10)(x^n - 2)$
Work Step by Step
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, $x^{2n} + 8x^n - 20$ = $(x^n + 10)(x^n - 2)$
