Question

Which expression is a factored form of 9x2 + 66x + 21?

Group of answer choices

3(3x – 1)(x + 7)

(3x + 1)(x + 7)

3(3x + 1)(x + 7)

3(3x – 1)(x – 7)

Answer 1

To factor the expression \(9x^2 + 66x + 21\), let's follow these steps:

1. **Look for common factors**: All coefficients (9, 66, 21) have a common factor of 3. We can factor this out:
\[
9x^2 + 66x + 21 = 3(3x^2 + 22x + 7)
\]

2. **Now, we will factor the quadratic \(3x^2 + 22x + 7\)**. We need two numbers that multiply to \(3 \cdot 7 = 21\) and add to \(22\). The numbers \(21\) and \(1\) fit this criterion.

3. **Rewrite and factor by grouping**:
\[
3x^2 + 21x + 1x + 7
\]
Grouping the first two terms and the last two:
\[
= 3x(x + 7) + 1(x + 7) = (3x + 1)(x + 7)
\]

4. **Putting it all together**:
Thus, the original expression factors to:
\[
9x^2 + 66x + 21 = 3(3x + 1)(x + 7)
\]

From the choices provided, the correct factored form of \(9x^2 + 66x + 21\) is:
\[
\boxed{3(3x + 1)(x + 7)}
\]