SOLUTION: what does it mean if P(-4) for the polynomial p(x)= x^3+4x^2-9x-36 equals zero?

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Question 1014980: what does it mean if P(-4) for the polynomial p(x)= x^3+4x^2-9x-36 equals zero?
Found 2 solutions by LinnW, rothauserc:
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
The original equation
p%28x%29=+x%5E3%2B4x%5E2-9x-36++
To evaluate P(-4) we substitute -4 for x
p%28-4%29=+%28-4%29%5E3%2B4%28-4%29%5E2-9%28-4%29-36+
Simplifying
p%28-4%29=+%28-64%29%2B4%2816%29%2B36-36+
p%28-4%29=+%28-64%29%2B64++
p%28-4%29=+0
As for the meaning, when x = -4,
The value of the function P(x) = 0

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
P(-4) means if you substitute x = -4 in
p(x) = x^3 +4x^2 -9x -36 = 0
:
(-4)^3 +4(-4)^2 -9(-4) - 36 = 0
-64 +64 +36 -36 = 0
0 = 0
:
this means that (x+4) is a factor of x^3 +4x^2 -9x -36
:
note that you can apply synthetic division to find the other factors