Question

Karen was trying to factor 6x^2+106x

2

+106, x, squared, plus, 10. She found that the greatest common factor of these terms was 222 and made an area model:



What is the width of Karen's area model?

Answer 1

3x^2+5

Step-by-step explanation:

I got it from khan academy

Answer 2

Step-by-step explanation:

Here we know that Karen was trying to factor the following expression:

`6x^2+106x`

And we want to find the width of Karen's area model, so we can say that that expression represents the area of a rectangle, so if we name (A) as this area, then:

`A=6x^2+106x \\ \\ \\ \text{Taking 2x as common factor}: \\ \\ A=2x(3x+53)`

Recall that the area of a rectangle is defined as:

`A=L* W \\ \\ \\ Where: \\ \\ L:Length \\ \\ W:Width`

So we can say:

`W=2x \\ \\ L=3x+53`

Finally, the width is:

`\boxed{2x \ units}`