Question

How do you write `12x^3-4x^2` in factored form?

Answer 1

`4x^2(3x-1)`

Explanation:

We "factorize" the two terms:

• `12x^3=2*2*3*x*x*x`
• `-4x^2=-1*2*2*x*x`

The common factors are `2`, `2`, `x`, and `x`. Combine (multiply) these to get `4x^2`.

We divide both terms by `4x^2`: `(12x^3)/(4x^2)=3x` and `(-4x^2)/(4x^2)=-1`. Thus, after factoring `4x^2` out, we will be left with `3x-1`.

This means that `12x^3-4x^2=4x^2(3x-1)`.

Answer 2

`12x^3-4x^2=color(green)(4x^2(3x-1))` or `color(green)((2x)^2(3x-1))`

Explanation:

Factor the constants and the variables of each term separately by finding the GCF (Greatest Common Factor) of each.

`GCF(12,4)=4`

`GCF(x^3,x^2)=x^2`

To string it out into (probably) excessive detail:

`color(red)(12x^3)-color(blue)(4x^2)`

`color(white)("XXX")=(color(red)(4 xx 3 xx x^2 xx x)) - (color(blue)(4 xx1 xx x^2 xx1))`

then using the distributive property (in reverse):
`color(white)("XXX")=(4xxx^2)((color(red)3 xx x)-(color(blue)(1xx1)))`

`color(white)("XXX")=4x^2(3x-1)`

Following this, you could further factor `4x^2` as `2^2x^2=(2x)^2`