Algebra: A Combined Approach (4th Edition)

Chapter 6 - Section 6.2 - Exercise Set: 94 (Answer) $x^{2n} + 5x^n + 6$ = $(x^n + 2)(x^n + 3)$
Chapter 6 - Section 6.2 - Exercise Set: 94 (Solution) Factorize : $x^{2n} + 5x^n + 6$ First, take $(x^{2n} + 5x^n + 6)$ to be $(x^n + \triangle)(x^n + \square)$ For this, we have to look for two numbers whose product is 6 and whose sum is 5. Factors of 6 $\Longleftrightarrow$ Sum of Factors 1,6 $\Longleftrightarrow$ 7 (Incorrect sum) 2,3 $\Longleftrightarrow$ 5 (Correct sum, the two numbers are 2 and 3) Thus, $x^{2n} + 5x^n + 6$ = $(x^n + 2)(x^n + 3)$