Question

How do you factor `25x ^ { 3} - 100x ^ { 2} - 9x + 36`?

Answer 1

We can split the entire expression into two parts and then combine the resulting binomials. This will give us our answer of `(25x^2-9)(x-4).`

Explanation:

Let's focus on `25x^3-100x^2` first. We can factor out `25x^2` from each term to get `25x^2(x-4)`. The other side, `-9x+36`, can have `-9` be factored out to give us `-9(x-4)`. Let's put our equation back together:

`25x^2(x-4)-9(x-4)`

How do we combine the binomials? Notice how `(x-4)` is a result of both parts. This will be one of our binomials. We also have `25x^2` and `-9` on the outsides of our parentheses. We'll put those two together to form our second binomial. Our answer is:

`(25x^2-9)(x-4)`

And here's a double check:

`(25x^2*x)+(25x^2*-4)+(-9*x)+(-9*-4)`
`25x^3-100x^2-9x+36` <----- Expression that we started with!