How do you factor trinomials?

Question

8x^2 - 4x - 24

Answer 1

ok, first of all, simplify the thing. Divide it all by 4. (8x^2 - 4x - 24 becomes 2x^2 - X - 6)

Now, factoring these things is generally guess and test.(unless you use a different method, such as the quadratic formula).

I'll leave it to someone else to explain what to do, as it can be confusing, but your answer would be (2x + 3) (x-2)

Answer 2

It basically is a trial and error method. Too many steps for me to explain here, but it involves finding the factors of - 24, the factors of 8, and then trying out various combinations of the factors until you get the trinomial. Practice makes it easier. In your example, one of the factors is 4 because it is a factor of all 3 terms. So initially you get the factors 4 and 2x^2 - x - 6. Then look at the factors of 6 and 2. Play with those factors until you come up with (2x + 3) and (x - 2). So the factors are 4, (2x + 3) and (x - 2). Well, I guess I did have time.

Answer 3

products of 24 that differ by 4 - whoops didn't see the 8 in front of the x^2

ummm ...

I'd do it by taking the 8 out the front and then messing with it a bit

yikes - okay - I wound up cheating and using the quadratic equation

8x^2 - 4x - 24

= 8 (x^2 - x/2 - 3)

I couldn't think off the top of my head what factors of 3 differ by 1/2

so ...

I found the roots by using x = (-b +/- SQRT(b^2 - 4ac))/2a the quadratic equation

and got 2 and -3/2

so... 8x^2 - 4x - 24 = 8(x-2)(x+3/2)

but there must be an easier way

Answer 4

Factor out the 4. Get 4(2x^2-x-6) then do the little circle thing and get 4(x+2) (x-3)

Answer 5

All have factor of 4

Answer 6

Honestly, it's all by trial and error. One easy thing to do is look for a common number that can divide itself into the numbers of the equation.
(4x+6)(2x-4) is the answer

Answer 7

4(2x^2-x-6) = 4(x-2)(2x+3)

Answer 8

4(2x^2-x-6)
4(2x+3)(x-2)

x=-3/2 or 2