Question

What are the zeros of the polynomial function f(x) = x3 − x2 − 12x?
a. 0,-4,-3
b. 0,-4,3
c. 0,4,-3
d. 0,4,3

Answer 1

Will fan and metal!!!

Answer 2

hint: \(\bf f(x)=x^3-x^2-12x\iff x(x^2-x-12)
\\ \quad \\
hint:\qquad -4\cdot 3=12\qquad \qquad -4+3=-1\)

use those hints, and we'll give you a medal :)

Answer 3

Can you walk me through the problem?

Answer 4

hmmm -12 I meant of course \(\bf f(x)=x^3-x^2-12x\iff x(x^2-x-12)
\\ \quad \\
hint:\qquad -4\cdot 3=-12\qquad \qquad -4+3=-1\)

Answer 5

-4 and 3 are factors of -12, the constant in the trinomial
use those factors to construct two binomials

then use FOIL to see if those two binomials give you the original trinomial :)

Answer 6

Im confused..

Answer 7

@sunnnystrong

Answer 8

@babe2323433 ..
Okay so basically you need to factor this out.

If
\[ f(x) = x^3 − x^2 − 12x\]
You can factor out an x & solve

\[ f(x) = x(x^2 − x − 12)\]
Now... you need to factor the quadractic:
What two #'s when added together =-1 & when multiplied = -12
---> gonna be -4 & 3

So:
\[ f(x) = x(x-4)(x+3)\]
Zeros of f are when x=3 so:
set each factor = 0 and solve for x

you get:
x=0 , x=4, x=-3
are the roots of f

Answer 9

Ohhhhhhhhhhhhh.. Omg thank you sooo much!!!!

Answer 10

NP Always happy to help lol :D

Answer 11

How do I give you a metal? @sunnnystrong

Answer 12

\(\begin{array}{llll}
x({\color{blue}{ x^2-x-12 }} )
\end{array}\implies
\begin{array}{cccllll}
x^2&-x&-12\\
&-4+3&-4\cdot 3
\end{array}
\\ \quad \\
thus\implies x^2-x-12\iff (x-4)(x+3)
\\ \quad \\
x({\color{blue}{ x^2-x-12 }} )\iff x{\color{blue}{ (x-4)(x+3) }}
\\ \quad \\
\textit{to get the zeros, set them to 0}
\\ \quad \\
0=x(x-4)(x+3)\implies
\begin{cases}
0=x&\to 0=x\\
0=x-4&\to 4=x\\
0=x+3&\to -3=x
\end{cases}\)

Answer 13

You click on the little metal lol

Answer 14

Ohh.. Lol
Can you help me with a few more?

Answer 15

yep just close and the question and post another one :D

Answer 16

yeah, you click on the "metal" to give it
just make sure is not rusty, otherwise you may give the other fellow a rash

now for the "medal", just click on "best response" button on the right :)