SOLUTION: Factor the trinomail completely. x squared - 11x

SOLUTION: Factor the trinomail completely. x squared - 11x - 60

Question 114212: Factor the trinomail completely.
x squared - 11x - 60
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You want to factor

This is a trinomial of the form where a = 1, so we only have to consider the factors of c and the sum of those factors that equal b.

Step 1:

Look at the sign on the constant term. In this case it is negative. That means that the factors of -60 in this case must be of opposite signs. Now we know that the factors of the trinomial are going to look like this:

(x + __ )
(x - __ )

Step 2:

We need to find two integers, call them p and q such that pq = -60 and p + q = -11. Let's start with some possibilities:
p * q = -60
-3 * 20 = -60
3 * -20 = -60
-4 * 15 = -60
4 * -15 = -60
-5 * 12 = -60
5 * -12 = -60
-6 * 10 = -60
6 * -10 = -60

Step 3:

-3 + 20 = 17
3 - 20 = -17
-4 + 15 = 11
4 - 15 = -11: Ah Ha!

Now, for each of the choices of p and q above, which pair, when added together will yield -11? The only pair that has a difference of 11 is 4 and 15, but since the result must be -11, the negative sign needs to be on the 15, so now we have our p and q and we can simply plug those numbers into our factor pattern we established in Step 1.

is the required factorization.

Last step -- VERY IMPORTANT. Check your answer.

Apply FOIL
. Checks.

Hope that helps,
John
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