Question

factor the following trinomial.
$3x^2 + 17x - 28$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. $3x^2 + 17x - 28 = \square$
b. the polynomial is prime.

Explanation:

Step1: Find product of first/last terms

$3 \times (-28) = -84$

Step2: Find pair summing to 17

We need two numbers that multiply to -84 and add to 17: $21$ and $-4$ (since $21 \times (-4) = -84$, $21 + (-4) = 17$)

Step3: Split middle term

$3x^2 + 21x - 4x - 28$

Step4: Factor by grouping

Group first two and last two terms:
$(3x^2 + 21x) + (-4x - 28) = 3x(x + 7) - 4(x + 7)$
Factor out $(x+7)$: $(3x - 4)(x + 7)$

Answer:

A. $3x^2 + 17x - 28=(3x-4)(x+7)$