SOLUTION: Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. x^3 + 2x^2 - 11x

SOLUTION: Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. x^3 + 2x^2 - 11x - 12 = 0; -

Question 166439: Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation.
x^3 + 2x^2 - 11x - 12 = 0; -4
o (3,1,-4)
o (3,-1,-4)
o (-3,1,-4)
o (-3,-1,-4)
Using a previous example given on this website, I believe the answer is the first choice given above, but am not certain.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
First, substitute x = -4:
=
Now, if x = -4 is a root, (and it is), then x+4 = 0 and x+4 is a factor of the given cubic equation.
So when you divide the given equation by the factor (x+4) you get:
so you now have:
Factor the trinomial.
Apply the zero product rule to get:

So the solution is:
(3, -1, -4) which is the second choice in the list of possible solutions.
This can be verified from the graph of the given equation.

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