Question

what is the completely factored form of this expression?
$3x^2 - 17x - 28$
a. $(3x + 4)(x + 7)$
b. $(3x + 4)(x - 7)$
c. $3x^2 - 17x - 28$
d. $(3x^2 + 4)(x - 7)$

Explanation:

Step1: Split middle term

Find two numbers that multiply to $3\times(-28)=-84$ and add to $-17$. These numbers are $4$ and $-21$. Rewrite the middle term:
$3x^2 + 4x - 21x - 28$

Step2: Group and factor pairs

Group the first two and last two terms, then factor out common terms:
$x(3x + 4) - 7(3x + 4)$

Step3: Factor out common binomial

Extract the shared binomial factor:
$(3x + 4)(x - 7)$

Step4: Verify options

Match the result to the given multiple-choice options.

Answer:

B. $(3x + 4)(x - 7)$