SOLUTION: Identify all the rational zeros for f(x)=x3(cubed)+4x2(squared)-3x-18

Question 7756: Identify all the rational zeros for f(x)=x3(cubed)+4x2(squared)-3x-18
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Find the zeros of:
Try factor by grouping:
Take the first set of parentheses:
is a difference of two cubes and can be factored as follows:
where: A = x and B = 2, then:

Now the second set of parentheses:
Factor:
So, altogether we have:

Now, factor out (x - 2):
Simplifying the 2nd parentheses:
Now factor the 2nd parentheses:
Now, set this equal to zero.
and apply the zero product principle:
, then; or
then: , and
So, the three zeros are:
x = 2, or x = -3 (a double root)
Take a look at the graph.

RELATED QUESTIONS
Identify all rational zeros for f(x) = x3 + 4x2 - 3x -... (answered by RAY100)

I really need help with this as fast as possible thanks alot! What are all the... (answered by solver91311)

Please lend me a helping hand. I would really appreciate your help and may God bless you... (answered by stanbon)

identify all rational zeros of the polynomial function... (answered by Fombitz)

x3(cubed)+4x2(squared)+4x (answered by stanbon)

Use the Rational Zero Theorem to list all possible rational zeros for the given function. (answered by lwsshak3)

Find all the rational zeros of the function. f(x) = x3 � 19x � 30 (answered by lwsshak3)

Identify the real zeros to the nearest tenth for the function f(x) = x3 - 6x - 9. (answered by khwang)

Find a rational zero of the polynomial function and use it to find all the zeros of the... (answered by sofiyac)