Question

how to factor a polynomial with a fraction. EX. x^2+7x+11

Answer 1

well , you can do this
x(x+7) +11

Answer 2

I think your best bet is to complete the square to solve for vertex or use the quadratic formula because its not factorable

Answer 3

If we have to use a perfect square, how would we do that?

Answer 4

You set it up like this:
(x^2 + 7x) + 11
You divide the coefficient of x which is 7 by 2. Square (7/2) and add it to both sides

Answer 5

So now you have (x^2 + 7x + 49/4) -49/4 + 44/4

Answer 6

(x + 7/2)^2 -5/4

Answer 7

Wait but how do you simplify x^2+7x+49/4, because I got up to this point, I dont' get what to do after...

Answer 8

You have to consider what multiply to 49/4 and add up to 7

Answer 9

okay because its an equation whatever you do to the right side must be applied to the left side...if initially you set up your equation equal to 0 then when you added 49/4 you will also add 49/4 to the right side

Answer 10

x^2 + 7x + 49/4 + 11 = 49/4

Answer 11

(x^2 + 7x + 49/4) becomes (x + 7/2)^2

Answer 12

And then you subtract 11 which is 44/4 from 49/4 = 5/4

Answer 13

So you have (x + 7/2)^2 - 5/4 = 0...do you understand it?

Answer 14

Oh! So the middle number is what you add to get and the last part of the equation (49/4) is what you multiply to get.

Answer 15

Yes, that's correct

Answer 16

Thank you you have been very helpful! is there a way I can +1 you or something? I just signed up so I have no clue how this works :S

Answer 17

you can "Good Answer" me

Answer 18

yes that's correct! Glad you understand