Questions: Factor out the Greatest Common Factor of the following polynomial. Select the two factors 5 x^2+5 x

Transcript text: Factor out the Greatest Common Factor of the following polynomial. Select the two factors \[ 5 x^{2}+5 x \]

Solution

Solution Steps

To factor out the Greatest Common Factor (GCF) of the polynomial \(5x^2 + 5x\), first identify the GCF of the coefficients and the variable terms. The GCF of the coefficients (5 and 5) is 5, and the GCF of the variable terms (\(x^2\) and \(x\)) is \(x\). Factor out the GCF from the polynomial.

Step 1: Identify the Polynomial

We start with the polynomial \(5x^2 + 5x\).

Step 2: Determine the GCF

The coefficients of the terms are 5 and 5, and the variable terms are \(x^2\) and \(x\). The Greatest Common Factor (GCF) of the coefficients is \(5\), and the GCF of the variable terms is \(x\).

Step 3: Factor Out the GCF

We can factor out the GCF from the polynomial: \[ 5x^2 + 5x = 5x(x + 1) \]