Name: Factoring trinomials: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 51 s
Description: Which of the following expressions is a factor of x² + 3x - 28? Try it, then watch the animated solution.

Factoring undoes multiplying. We want

(x + p)(x + q)

whose four parts add up to

x^2 + 3x - 28

.

The two

x

parts must add to

3x

, so

p + q = 3

. The last part must be

{-28}

, so

p \cdot q = {-28}

.

Try pairs that multiply to

{-28}

with the larger number positive. Only

{-4}

and

7

add to

3

.

So

x^2 + 3x - 28 = (x + 7)(x - 4)

. Of the choices, only

x - 4

is one of these two factors.

Traps:

x - 7

and

x + 4

have the signs switched, and

x + 3

uses the sum, not one of the numbers.

Try it first