Question

Pascha is factoring the polynomial, which has four terms.

3x3 – 15x2 + 8x – 40


3x2(x – 5) + 8(x – 5)


Which is the completely factored form of her polynomial?


(3x2 – 5) (x + 8)

(3x2 – 8) (x + 5)

(3x2 + 8) (x – 5)

(3x2 + 5) (x – 8)

Answer 1

c

Explanation:

Answer 2

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

Explanation:

Given

`3x^3 - 15x^2 + 8x - 40 = 3x^2(x - 5) + 8(x - 5)`

Required

Complete the factorization

`3x^3 - 15x^2 + 8x - 40 = 3x^2(x - 5) + 8(x - 5)`

When an equation is factorized as:

`a(b + c) + d(b + c)`

The complete expression is:

`(a + d)(b + c)`

Apply this logic in
`3x^3 - 15x^2 + 8x - 40 = 3x^2(x - 5) + 8(x - 5)`

By comparison:

`a = 3x^2; b = x; c = -5; d = 8`

So, we have:

`3x^3 - 15x^2 + 8x - 40 = (3x^2 + 8)(x - 5)`

Hence,

`(3x^2 + 8)(x - 5)` is the complete factor