Question

Which is the completely factored form of 12x3 – 60x2 + 4x – 20?

Answer 1

`4(x-5)(3{x}^(2)+1)`

Explanation:

1) Find the Greatest Common Factor (GCF).

1 - What is the largest number that divides evenly into
`12x^3,-60x^2,4x,` and
`-20` ?

It is
`4.`

2 - What is the highest degree of
`x` that divides evenly into
`12x^3,-60x^2,4x,` and
`-20` ?

It is 1, since
`x` is not in every term.

3 - Multiplying the results above,

The GCF is 4.

2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

`4(\frac{12{x}^(3)}{4}+\frac{-60{x}^(2)}{4}+(4x)/(4)-(20)/(4))`

3) Simplify each term in parentheses.

`4(3{x}^(3)-15{x}^(2)+x-5)`

4) Factor out common terms in the first two terms, then in the last two terms.

`4(3{x}^(2)(x-5)+(x-5))`

5) Factor out the common term
`x-5`.

`4(x-5)(3{x}^(2)+1)`