Question

factor the polynomial $2x^2 + 9x + 9$.

select one:
a. $(x + 3)(2x + 3)$
b. $2(x^2 + 9x + 9)$
c. $(x - 3)(2x + 3)$
d. $(x + 3)(2x - 3)$

Explanation:

Step1: Split middle term

Find two numbers that multiply to $2\times9=18$ and add to $9$. The numbers are 6 and 3.
Rewrite polynomial: $2x^2 + 6x + 3x + 9$

Step2: Group and factor pairs

Group first two and last two terms: $(2x^2 + 6x) + (3x + 9)$
Factor out GCF from each group: $2x(x + 3) + 3(x + 3)$

Step3: Factor common binomial

Factor out $(x+3)$ from both terms: $(x + 3)(2x + 3)$

Step4: Verify options

Match result to given choices.

Answer:

A. $(x + 3)(2x + 3)$