Question

The area of a rectangle is represented by 3x^2 + 14x + 8. Factor the area to determine the dimensions of the rectangle.

Answer 1

(3x+2)(x+4)

Explanation:

(3x+2)(x+4) = (3x)(x) + (3x)(4) + (2)(x) + (2)(4)

= 3x² + 12x + 2x + 8 *****

= 3x² + 14x + 8

You start by figuring it will be in the form of (3x + a)(x + b) because 3 doesn't factor. The two middle terms in the line followed by the stars must add up to 14x. And in (3x + a)(x + b), ab must be equal to the 8 on the end (the constant factor).

For most people, factoring takes a LOT of practice. And somethimes you just have to try a lot of factors before you hit the right combination. But if you do it enough, it really does get easier to 'see' the answer a lot of the time.

Hope this helped!