Question

GCF factoring introduction

Got
Averi was trying to factor 4x^2 + 20x – 16. She found that the greatest common factor of these terms was 4
and made an area model:

What is the width of Averi's area model?

Answer 1

16

Explanation:

Answer 2

`\large \boxed{x^(2) + 5x - 4}`

Explanation:

One way to make an area model for this question is:

• Divide a rectangle into three parts.
• Write the common factor on the left-hand side.
• Write one term of the polynomial in each box.

The area of each box is

A = lw. Then,

w = A/l

To get the width of each box, we divide its area by its length — the common factor, 4.

For the green box, w = 4x²/4 = x²

For the brown box, w = 20x/4 = 5x

For the yellow box, w = -16/4 = - 4

For the whole rectangle, w = x² + 5x - 4

`\text{The width of their area model is $\large \boxed{\mathbf{x^(2) + 5x - 4}}$}.`