Question

How do you factor `15x^2+6x`?

Answer 1

`3x(5x + 2)`

Explanation:

Given: `15x^2 + 6x`

To factor you find the greatest common factor (GCF) of each term.

`15 x^2 = color(red)(3) * 5 * color(red)(x) * x`

`6x = 2 * color(red)(3) * color(red)(x)`

The GCF is `3x`

Factor using GCF: `3x ( 5x + 2)`

Answer 2

`3x(5x+2)`

Explanation:

`15x^2+6x`
=
`3*5*x*x + 3*2*x`

As you can see, both terms have a three, and at least one x.

So we can start by pulling out a three:

`15x^2+6x`
=
`3(5x^2+2x)`

And finally we can pullout one x, since both terms have at least one:

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

We can test are answer by multiplying the `3x` by both terms in the parentheses, and seeing if we get our original expression:

`3x(5x+2)`
=
`3x*5x + 3x*2`
=
`15x^2 +6x`

So, `3x(5x+2)` is correct.