Question

What is the factorization of 2x2 + 9x + 9?

(x + 3)(x + 3)

(2x + 3)(x + 3)

(x + 3)(x + 9)

(2x + 1)(x + 3)

Answer 1

To factor the quadratic expression \(2x^2 + 9x + 9\), we can use the method of factoring by grouping or find two numbers that multiply to \(2 \cdot 9 = 18\) (the product of the coefficient of \(x^2\) and the constant term) and add up to \(9\) (the coefficient of \(x\)).

The two numbers that work here are \(6\) and \(3\) since:

\[
6 + 3 = 9, \quad 6 \cdot 3 = 18
\]

Now, we can rewrite the middle term \(9x\) using \(6x\) and \(3x\):

\[
2x^2 + 6x + 3x + 9
\]

Next, we group the terms:

\[
(2x^2 + 6x) + (3x + 9)
\]

Factoring out the common factors from each group:

\[
2x(x + 3) + 3(x + 3)
\]

Now, we see that \((x + 3)\) is a common factor:

\[
(2x + 3)(x + 3)
\]

So, the factorization of \(2x^2 + 9x + 9\) is:

\[
(2x + 3)(x + 3)
\]

This matches one of the given options. Therefore, the correct answer is:

\((2x + 3)(x + 3)\)