Question

Factor completely x2 + 20x − 36.

Answer 1

Explanation:

To do this, identify a, b, and c of the quadratic.

a = 1, b = 20, c = |-36|

Find a*c. That's 36. Now find the factors of 36 and the 2 factors that can combine to give you b, which is 20, are the ones we want.

36: 1, 36

2, 18

3, 12

4, 9

6, 6

The ones that combine to give you 20 are 2, 18. Both positive. Therefore,

`x^2+18x+2x-36` is how you begin to factor. Factoring by grouping is the way to go.

`(x^2+18x)+(2x-36)`

Factor out what you can from each set of parenthesis:

x(x + 18) + 2(x + 18)

What's common now is what's inside the parenthesis, so that gets factored out:

(x + 18)(x + 2)

That's factored completely!