Answer
Chapter 6 - Section 6.2 - Exercise Set: 87 (Answer)
$z^2(x + 1) - 3z(x + 1) - 70(x + 1)$ = $(x + 1)(z - 10)(z + 7)$
Work Step by Step
Chapter 6 - Section 6.2 - Exercise Set: 87 (Solution)
Factorize : $z^2(x + 1) - 3z(x + 1) - 70(x + 1)$
First step : Take out the GCF $(x + 1)$.
$z^2(x + 1) - 3z(x + 1) - 70(x + 1)$ = $(x + 1)(z^2 - 3z - 70)$
Take $(z^2 - 3z - 70)$ to be $(z + \triangle)(z + \square)$
For this, we have to look for two numbers whose product is -70 and whose sum is -3.
Factors of -70 $\Longleftrightarrow$ Sum of Factors
1,-70 $\Longleftrightarrow$ -69 (Incorrect sum)
2,-35 $\Longleftrightarrow$ -33 (Incorrect sum)
5,-14 $\Longleftrightarrow$ -9 (Incorrect sum)
7,-10 $\Longleftrightarrow$ -3 (Correct sum, so the two numbers are 7 and -10)
… no need to consider more trials as 7 and -10 matched the criteria already
Thus, $z^2(x + 1) - 3z(x + 1) - 70(x + 1)$ = $(x + 1)(z - 10)(z + 7)$