Question

factor out the greatest common factor.
$9x^4 - 31x^3 - 52x$
$?(9x^3 - 31x^2 - 52)$

Explanation:

Step1: Identify GCF of terms

Find GCF of $9x^4$, $31x^3$, $52x$:

• Coefficients: GCF of 9, 31, 52 is 1
• Variables: GCF of $x^4$, $x^3$, $x$ is $x$

Combined GCF: $1 \times x = x$

Step2: Verify factoring

Divide each term by $x$:
$\frac{9x^4}{x}=9x^3$, $\frac{-31x^3}{x}=-31x^2$, $\frac{-52x}{x}=-52$
This matches the given factored form's parentheses.

Answer:

$x$