Q. 6.16 - Intermediate Algebra

Question

Factor by grouping:

a) $y^2+4y-7y-28$

b) $42m^2-18m-35m+15$

Step-by-Step Solution

Answer

a) The factored form is $(y+4)(y-7)$.

b) The factored form is $(7-3m)(6m-5)$.

Part (a) Step 1. Given Information

The given expression is $y^2+4y-7y-28$.

Part (a) Step 2. Rewrite the given expression

• All four terms do not have the greatest common factor.
• Factor the GCF, $y$ from the first 2 terms of the given expression.

$y(4+y)-7y-28$

• Factor the GCF, $-7$ from the last two terms of the obtained expression.

$y(y+4)-7(y+4)$

• Factor out the common factor $y+4$ in the obtained expression.

$y(y+4)-7(y+4)=(y+4)(y-7)$

Part (b) Step 1. Given Information

The given expression is $42m^2-18m-35m+15$.

Part (b) Step 2. Rewrite the given expression

• All four terms do not have the greatest common factor.
• Factor the GCF, $6m$ from the first 2 terms of the given expression.

$6m(7-3m)-35+15$

• Factor the GCF, $-5$ from the last two terms of the obtained expression.

$6m(7-3m)-5(7-3m)$

• Factor out the common factor $7-3m$ in the obtained expression.

$6m(7-3m)-5(7-3m)=(7-3m)(6m-5)$