Help please! I have to show my work.. x^2+8x+15/x+3?

Answer 1

[x^2+8x+15] / (x+3)

step 1) factor numerator into:

(x+3)(x+5)

to get:

[(x+3)(x+5)] / (x+3)

step 2) cancel the (x+3) from both the numerator & denominator and you are left with:

( x+5 ) / 1 = x + 5

as your final answer.

Answer 2

x^2+8x+15 = (x+3)(x+5)
x^2+8x+15/x+3 =(x+3)(x+5)/(x+3) = x+5

Answer 3

x^2+8x+15 /x+3
(x+5)(x+3) / (x+3)
x+5
I suspect that factoring x^2 +8x +15 threw you a bit.
You have also probably heard of "FOIL". It's an acronym for remembering how to multiply two binomials.
F=First terms
O=Outside terms
I=Inside terms
L=Last terms

Let's apply this to (x+5)(x+3)
F=(x)(x)=x^2
O=(x)(3)=3x
I=(5)(x)=5x
L=(5)(3)=15
Add, x^2+3x+5x+15=x^2+8x+15
Which was in your original problem.
To factor x^2 +8x+15, you "un-FOIL " it
We know that an expression with x^2 in it as the highest power is going to have two factors. they will look like this:
(?......?)(?......?)
F will have to be x's. We want +1x when we multiply the first terms. So we have
(x....?)(x.....?)
The two ? have to be two numbers that multiply to give 15 AND ADD UNDER O and I to give 8
15 and 1 is one option, but I can't make them combine under O and I to give 8
5 and 3 is another option and they work!
I thus have (x+5)(x+3)

I hope this helps.

Answer 4

1) factor numerator (x+3)(x+5)

[(x+3)(x+5)] / (x+3)

2) cancel(x+3) from up and down
you find x + 5 left