Question

Simplify completely:

2x^2 + 13x + 20
________________
x^2 - 5x - 36

Answer 1

First factor the numerator and denominator.

Answer 2

how????

Answer 3

In the numerator you have a trinomial of the type
ax^2 + bx + c
First multiply ac. In your case that is 2 and 20

Answer 4

ac = 40.
Now find two factors of ac that add up to b.
In this case, find 2 factors of 40 that add up to 13

Answer 5

10 x 4

Answer 6

10 and 4 are factors of 40 but don't add to 13.
8 and 5 are factors of 40 that add to 13.
Now you take 8 and 5 and you break the middle term into 8x and 5x.
2x^2 + 8x + 5x + 20
Now factor a common factor out of the first two terms and a common factor out of the last two terms.
2x(x + 4) + 5(x + 4)
Now pull out the common factor of x + 4, so you end up with
(x + 4)(2x + 5) This is the factorization of the nemerator.

Now you need to factor the denominator.
You need 2 numbers that multiply to -36 and add to -5.
The numbers are -9 and 4.
It factors into:
(x - 9)(x + 4)

The final answer is
(2x + 5) / (x - 9)