Question

Factor 5x 4 - 30x 2 - 135. 5(x2 + 9)(x2 - 3) 5(x - 3)(x + 3)(x2 - 3) 5(x - 3)(x + 3)(x2 + 3)

Answer 1

Explanation:

`5x^(4) -30x^(2) -135`

We need to pull out 5 to make the rest easier to factor.

`5(x^(4) -6x^(2) -27)`

Now we can factor.

Consider all combinations of how to get 27.

1 x 27

3 x 9

And that's it before you end up just switching the place i.e. 9 x 3 and 27 x 1

This makes it easy to see that 3 and 9 are our best choice because 9 - 3 is 6 which is our middle term in the equation.

So now we have:

`5(x^(2) -9)(x^(2) +3)`

We can break down
`x^(2) -9` even further because it's a perfect square.

(x - 3)(x + 3)

Our final factor is

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