Question

Factor 6x^3 + 33^2 - 63x

Answer 1

This factors out to
`3x (x + 7) (2x - 3)=0`.

First, notice that the greatest common factor of this set is
`3x`.

Once you factor that out, you have a quadratic
`2x^2+11x-21=0`.

You can solve this by factoring using the ac method, to find two factors whose product is -42 and whose sum is 11. These factors are 14 and -3.

You can split the middle term b to write
`2x^2+14x-3x-21=0`.

Then, you can factor to write
`2x(x+7)-3(x+7)=0 \\ (2x-3)(x+7)=0`. Finally, don't forget the 3x from earlier!

This factors out to
`3x (x + 7) (2x - 3)=0`.