Question

Can someone explain to me what exactly I am doing with this problem? My lesson on this doesn't make sense and I can't find anywhere to get help on showing me how to solve this.

Determine the zeros of f(x) = x3 – 3x2 – 16x + 48

Answer 1

zeros means values of x for which f(x)=0
x3-3x2-16x+48=0
x2(x-3)-16(x-3)=0
(x-3)(x2-16)=0
(x-3)(x+4)(x-4)=0

so the zeroes are 3,4 and -4.

Answer 2

How do you figure out what x is?

Answer 3

if product of a few no. is zero that means one of the numbers is zero.
so either x-3 =0 (which would mean x=3)
or x+4 =0 meaning x=-4
or x-4=0 meaning x=4

Answer 4

How do you get to the 3, 4, -4

Answer 5

by solving the eq.

first we factorise the eq. and then equate each factor to zero

because one of them has to be zero