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

1 Answer
Jun 26, 2018

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!