Question

factor the polynomial $12x^2 + 11x + 2$.
select one:
a. $4x + 1(3x + 2)$
b. $(4x + 1)(3x - 2)$
c. $(4x + 1)(3x + 2)$
d. $12(x^2 + 11x + 2)$

Explanation:

Step1: Split middle term

Find two numbers that multiply to $12\times2=24$ and add to 11. The numbers are 8 and 3. Rewrite the polynomial:
$12x^2 + 8x + 3x + 2$

Step2: Group and factor pairs

Group the first two and last two terms, then factor out GCFs:
$4x(3x + 2) + 1(3x + 2)$

Step3: Factor common binomial

Factor out the shared binomial $(3x+2)$:
$(4x + 1)(3x + 2)$

Step4: Verify options

Compare the result to the given choices to confirm the match.

Answer:

C. $(4x + 1)(3x + 2)$