Question

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

Explanation:

Step1: Identify GCF of terms

The terms are $9x^4$, $-31x^3$, $-52x$. The GCF of coefficients 9, 31, 52 is 1. The GCF of $x^4$, $x^3$, $x$ is $x^1 = x$.

Step2: Verify factored form

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 expression $x^? (9x^3 - 31x^2 - 52)$, so the exponent of $x$ is 1.

Answer:

$1$