Question

How can I find the x-intercept of
f(x)= x^3 +12x^2-36x-432 ?

Please explain step by step.

Answer 1

You could try to eyeball which values make the function zero. However, if you try to solve \(x^3+12x^2-36x-432=0\) algebraically, you can do so by attempting to factor the cubic. In this case, it happens to work out; in particular, you would want to factor by grouping:
\[\begin{aligned} x^3+12x^2-36x-432 &= (x^3+12x^2) + (-36x-432) \\ &= x^2(x+12) -36(x+12)\\ &= (x^2-36)(x+12)\\ &= (x+6)(x-6)(x+12) \end{aligned}\]Therefore \(x^3+12x^2-36x-432 = 0 \implies (x+6)(x-6)(x+12) = 0\). So what solutions do you get?

I hope this makes sense! :-)

Answer 2

Are you a teacher?

Answer 3

Not really, but I'm applying to community colleges to become one. XD

Answer 4

(to become a professor, that is)

Answer 5

Be my private tutor please.

Answer 6

I'm currently taking Alg 2 and I'm almost at my final and I'm so cared.

Answer 7

this is just a grade 9 question here in India :)

Answer 8

It should be the same for the US...

Answer 9

Okay I'm a little confused I understand the steps but what are the x-intercepts?

Answer 10

I know it is an easy question but I just can't really remember, ATM

Answer 11

So, what we found are the zeros; the x values where the function is zero. However, the x intercepts are coordinates of the form (x,0). So you have three different x values that cause the function to be zero, and hence you have three coordinates. Can you see what they should be now? :-)

Answer 12

the intercepts are -6 6 and -12

Answer 13

silly me okay I got it.