Question

Can someone please explain how to solve this?
Simplify completely quantity 2 x squared plus 13 x plus 20 all over x squared minus 5 x minus 36.
I know you're supposed to find the greatest common factor or find the numbers that come out to 20 and add up to 13, but what about when you cant do either?

Answer 1

\[\frac{2x^2+12x+20}{x^2-5x-36}\]?

Answer 2

The 12 should be a 13 :)

Answer 3

\[\frac{2x^2+13
x+20}{x^2-5x-36}\]

Answer 4

Yup

Answer 5

idea is to factor the numerator and denominator, then cancel any common factors

Answer 6

for example, the denominator is \[x^2-5x-36=(x+4)(x-9)\]

Answer 7

when you factor the numerator, one of the factors will also be \(x+4\)
try it
then you can cancel

Answer 8

Thats kinda what I'm confused on the most, factoring when theres 3 numbers in the numerator

Answer 9

gonna factor like this
\[2x^2+13x+20=(x+4)(2x+something)\]

Answer 10

if you want a big hint, the product of the "something" and 4 has to be 20

Answer 11

So 5?

Answer 12

yeah 5 you can check by multiplication that
\[(x+4)(2x+5)=2x^2+13x+20\]

Answer 13

so you have
\[\frac{(x+4)(2x+5)}{(x+4)(x-9)}\] then cancel

Answer 14

So its 2x+5 over x-9?

Answer 15

yes it is

Answer 16

Is there an easy way to remember the steps to factor?

Answer 17

no
just have to grind it till you find it

Answer 18

you can start with
\[(x+a)(2x+b)\] for the first one, because you know what \(x\times 2x=2x^2\)
and you will also know that \(ab=20\) but there are several ways to factor 20
just turns out 4 and 5 work for this one

Answer 19

Ah alright, thank you so much :)