Factor the GCF out of:6x2+9x6x^2+9x

3 x ( 2 x + 3 ) 3x\left(2x+3\right)

Factor the GCF out of: 6 x 2 + 9 x 6x^2+9x

Here, we're asked to factor the polynomial six x squared plus nine x by factoring out the greatest common factor. So first, let's identify what the greatest common factor is. To do that, we're going to write out the prime factorization for each of our terms. The prime factors for six x squared are two times three times x times x, and the prime factors for nine x are three times three times x. So the factors that they have in common are three and x, which means our greatest common factor is three times x. So now I'm going to rewrite each of the terms in our polynomial as a product with the greatest common factor. So what can I multiply three x by to get six x squared? Well that would be two x, so I can rewrite it as three x times two x. And what can I multiply three x by to get nine x? Well, that would be three. So I can rewrite nine x as three x times three. Now I'm going to factor out three x, and I'm left with two x plus three. So this here is our final answer.

Factor the GCF out of: 6 x 2 + 9 x 6x^2+9x

3 x ( 2 x + 3 ) 3x\left(2x+3\right)

3 ( 2 x 2 + 3 x ) 3\left(2x^2+3x\right)

6 x ( x + 3 ) 6x\left(x+3\right)

3 x ( 2 x + 6 ) 3x\left(2x+6\right)

7. Factoring

Factoring by Greatest Common Factor & Grouping

Beginning Algebra

7. Factoring

Factoring by Greatest Common Factor & Grouping

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Multiple Choice

Factor the GCF out of:
$6 x squared plus 9 x$

$3 x (2 x + 3)$

$3 (2 x^{2} + 3 x)$

$6 x (x + 3)$

$3 x (2 x + 6)$

Verified step by step guidance

Identify the terms in the expression: \$6x^2 + 9x$.

Find the greatest common factor (GCF) of the coefficients 6 and 9. The GCF is the largest number that divides both 6 and 9 evenly.

Look at the variable parts: $x^2$ and $x$. Determine the lowest power of $x$ that appears in both terms, which will be part of the GCF.

Write the GCF by combining the GCF of the coefficients and the lowest power of $x$. This will be the factor you take out of the expression.

Factor the GCF out of each term inside the parentheses by dividing each term by the GCF, and write the expression as $\text{GCF} \times (\text{remaining terms})$.

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