Question

question
factor completely.
$3x^2 - 14x + 15$

Explanation:

Step1: Find product and sum

We need two numbers that multiply to $3\times15=45$ and add to $-14$. These numbers are $-9$ and $-5$.

Step2: Split the middle term

Rewrite the middle term using the two numbers:
$3x^2 -9x -5x +15$

Step3: Group and factor pairs

Group the first two and last two terms, then factor out the GCF from each group:
$3x(x - 3) -5(x - 3)$

Step4: Factor out common binomial

Factor out the shared binomial $(x-3)$:
$(3x - 5)(x - 3)$

Answer:

$(3x - 5)(x - 3)$