Factor this trinomial x2 plus 2x-15 equals?

Answer 1

You need to factor the following trinomial:

x2 + 2x - 15

In other words, you want to find an expression in this form, which is equal to the trinomial:

(A + B)(C + D)

Finding the values for A, B, C, and D is mostly a trial-and-error process, but here are a few tips that are helpful for situations such as this:

• AC (A times C) equals the number of the highest order in the trinomial (in this case, x2)
• BD equals the number of the lowest order in the trinomial (in this case, -15)
• AD plus BC equals the remaining number in the trinomial (in this case, 2x)

Since A times C equals x2, we know that we have something like this:

(x + B)(x + D)

Now, we also know that -3 times 5 is -15, and -3 plus 5 is 2. So, we have found the following:

(x - 3)(x + 5)

You can use the FOIL pattern (multiply the First numbers, then the Outside, Inside, and Last numbers and add together) to check that this factorization is correct:

(x - 3)(x + 5)

= AC + AD + BC + BD

= x2 + 5x - 3x - 15

= x2 + 2x - 15

It looks like that's the right answer. So, the factorization of this trinomial is (x - 3)(x + 5).