Question

Describe the steps you would use to factor

2x3 + 5x2 - 8x - 20 completely. Then state the
factored form.
I

Answer 1

• 2x³ + 5x² - 8x - 20

Putting the terms, which have something in common, in brackets:

• (2x³ + 5x²) - (8x - 20)

Factor them by taking the common terms outside the bracket.

• => x²(2x + 5) - 4(2x + 5)

Factor by taking the common expression out of the brackets:

• => (2x + 5)(x² - 4)

The multiplier (x² - 4) is in squared form.

Square root the multiplier of (2x + 5)(x² - 4), aka (x² - 4):

• => (2x + 5)(x - 2)(x + 2)

The factorized form is (2x + 5)(x - 2)(x + 2).

Answer 2

Factor by Grouping

2
`x^(3)` + 5
`x^(2)` - 8x - 20

2
`x^(3)` + 5
`x^(2)`

`x^(2)` (2x + 5)

-8x - 20

-4 (2x + 5)

(2x + 5) (
`x^(2)` - 4)

(2x + 5) (x - 2) (x + 2)