Question

factor out the greatest common factor.
10x² + 20x - 5
?(2x² + 4x - 1)

Explanation:

Step1: Recall GCF factoring

To factor out the GCF, we divide each term by the GCF. Let the GCF be \( a \), so \( 10x^2 + 20x - 5 = a(2x^2 + 4x - 1) \). We find \( a \) by dividing \( 10x^2 \) by \( 2x^2 \), \( 20x \) by \( 4x \), or \( -5 \) by \( -1 \).

Step2: Calculate the GCF

Dividing \( 10x^2 \) by \( 2x^2 \): \( \frac{10x^2}{2x^2} = 5 \). Check with other terms: \( \frac{20x}{4x} = 5 \), \( \frac{-5}{-1} = 5 \). So \( a = 5 \).

Answer:

5