Question

0=x^2+13x-30
I believe it is asking me to factor?

Answer 1

The factorization of this polynomial would be 0 = (x - 2)(x + 15)

In order to find it, we must look for factors of the last number (-30) that add up to the middle number (13). To do this, first list all the factors of -30.

1 and -30

-1 and 30

2 and -15

-2 and 15

3 and -10

10 and -3

5 and -6

-5 and 6

When you consider all of these factors, you can see only one of them adds up to 13 (-2 and 15). As a result, you place each of those numbers in a parenthesis with an x and multiply them together.

0 = (x - 2)(x + 15)

Answer 2

x² + 13x - 30 = 0

first, to factor this, we need to find 2 numbers, that when added, equal 13. These same numbers must also multiply to equal -30

15 and -2 fit this criteria.

15 + -2 = 13

15 x -2 = -30

now we can put these numbers in place of 13 in our equation

x²-2x+15x-30=0

now we take the common value of the fist 2 numbers and place it on the outside. we do the same with the last 2 numbers.

x(x-2) +15(x-2) = 0

notice how the numbers in parentheses are the same. we can now take the outside numbers and have them with the numbers in parentheses.

(x+15)(x-2) = 0

this is the factored form.

if you needed to find x, you take the numbers that would make one of the parentheses equal 0

so x = -15, 2

hope this helps