## anonymous one year ago f(x) = 6x2 - x - 12 and g(x) = 2x - 3 find the function (f/g)(x)

1. UsukiDoll

$f(x) = 6x^2-x-12$ $g(x) = 2x-3$ If your question is just asking to find the function $\frac{f(x)}{g(x)}$ then we just place the f(x) here ------------------ place the g(x) here the notation I'm using is the same as (f/g)(x)

2. anonymous

But I can't simplify 6x^2 - x -12. So there is no real answer for this equation?

3. UsukiDoll

we could try to simplify 6^x-x-12 using b^2-4ac which is the discriminant.

4. UsukiDoll

(-1)^2-4(6)(-12) for a = 6, b = -1, and c = -12

5. UsukiDoll

if we have a perfect square number like 25 16 9 then we can factor if we have a non-perfect square number like 3 -32... then we can't factor and have to use the quadratic equation (or just leave the problem alone in this case)

6. UsukiDoll

so from the discriminant (-1)^2-4(6)(-12) = 1-24(-12) =1+288 =289 we have a perfect square .. because the square root of 289 is 17

7. UsukiDoll

so we can factor 6x^2-x-12... it becomes (2x-3)(3x+4)

8. anonymous

Oh okay. so then the 2x -3 crosses each other out which leaves 3x+4?

9. UsukiDoll

yes! that's right! the 2x-3 terms cancels out

10. UsukiDoll

$\frac{(2x-3)(3x+4)}{2x-3} \rightarrow 3x+4$

11. anonymous

Okay so if the question is Given f(x) = x + 2 and g(x) = x2 - 4, find the function (fg)(x) then the answer would be x^3 -2x^2- 4x - 8

12. anonymous

Or did I do that wrong? Sorry. Still trying to get the hang of this

13. UsukiDoll

so (fg(x) or f(x)(g(x)) means that we multiply the f(x) function with the g(x) function

14. UsukiDoll

f(x)(g(x) = $(x+2)(x^2-4)$ then we use foil method

15. UsukiDoll

$x^3-4x+2x^2-8$

16. UsukiDoll

you've done it right....it's just that my terms have been rearranged. It means the same thing

17. anonymous

Okay got it! Thank you so much