Question

factor the trinomial, if possible.
$6k^2 + 5kp - 21p^2$

Explanation:

Step1: Identify trinomial form

We have a quadratic trinomial in two variables: $6k^2 + 5kp - 21p^2$, which follows the form $ak^2 + bkp + cp^2$.

Step2: Find factor pairs

We need two numbers that multiply to $6\times(-21) = -126$ and add to $5$. These numbers are $14$ and $-9$.

Step3: Split the middle term

Rewrite the middle term using the two numbers:
$6k^2 + 14kp - 9kp - 21p^2$

Step4: Factor by grouping

Group the first two and last two terms, then factor out the GCF from each group:
$2k(3k + 7p) - 3p(3k + 7p)$

Step5: Factor out common binomial

Factor out the shared binomial factor:
$(2k - 3p)(3k + 7p)$

Answer:

$(2k - 3p)(3k + 7p)$