Question

factor out the greatest common factor in the following polynomial.
$x^4 - 8x^3 + x^2 = \square$
check
explain

Explanation:

Step1: Identify GCF of coefficients and variables

For coefficients (1, -8, 1), GCF is 1. For variables: \(x^4 = x^2 \cdot x^2\), \( -8x^3 = x^2 \cdot (-8x)\), \(x^2 = x^2 \cdot 1\). So GCF is \(x^2\).

Step2: Factor out \(x^2\)

Divide each term by \(x^2\): \(\frac{x^4}{x^2}=x^2\), \(\frac{-8x^3}{x^2}=-8x\), \(\frac{x^2}{x^2}=1\). So \(x^4 - 8x^3 + x^2 = x^2(x^2 - 8x + 1)\).

Answer:

\(x^2(x^2 - 8x + 1)\)