x^2+x-12 in factored form?

Question

i'm stuck...
could someone please explain to me how to write x^2+x-12 in factored form?

i know that two numbers must add up to x and the same numbers must equal -12 if multiplied

i'm just confused on how to represent x...would it equal the same x that is squared?

(x+?)(x-?)

thanks!

omg i can't believe i didn't see that, i could have figured that out on my own! sorry for wasting your time. heh, i was overanylizing it, thinking i had to represent x instead of just finding the numbers....jeez.

Answer 1

A polinomial like x^2 + x - 12 can many times be factorized in a quite easy way if you consider that x^2 - s x + p, where s is the sum of the 2 roots and p is their product

In this case, s = -1 and p = -12

So, the roots will be one positive and one negative

3*4 = 12

But, since one root must be negative, and Im not sure if its -3*4 or 3*(-4) until I check the sign of s.

-3 + 4 = 1

But

3 - 4 = -1

Since s is negative, the second option is the right one

So: the polinomial is factorized this way: (x-root1)(x-root2)

In this case: (x + 4)(x-3) = x^2 + x - 12

Ana

Answer 2

x^2 + x - 12

what times what is -12 and adds to positive one
-3 and 4 right

(x+4) (x-3)

Answer 3

The factored form should be
(x+4)(x-3)

Multiply them up and u will get
x^2 + x -12

Answer 4

(x+4)(x-3)

Answer 5

You have the right idea.
(x+4)*(x-3) = x² + x -12
Factoring is mostly just a lot of practice.


Doug

Answer 6

(x + 4).(x - 3) as you said.
NB: 4x - 3x = x and (4) x (- 3) = - 12

Answer 7

(x-3)(x+4)

x^2+4x-3x-12
x^2+x-12