Question

factor the trinomial.
b² - bg - 42g²
b² - bg - 42g² = \square

Explanation:

Step1: Find pair of factors for -42

We need two numbers that multiply to $-42$ and add to $-1$. These numbers are $-7$ and $6$, since $(-7)\times6=-42$ and $-7+6=-1$.

Step2: Split the middle term

Rewrite the trinomial by splitting the $-bg$ term using the factors from Step1:
$b^2 -7bg +6bg -42g^2$

Step3: Factor by grouping

Group the first two and last two terms, then factor out the greatest common factor from each group:
$(b^2 -7bg) + (6bg -42g^2) = b(b-7g) + 6g(b-7g)$

Step4: Factor out common binomial

Factor out the shared binomial $(b-7g)$:
$(b-7g)(b+6g)$

Answer:

$(b-7g)(b+6g)$