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; -

Algebra ->  Polynomials-and-rational-expressions -> 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; -      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
First, substitute x = -4:
%28-4%29%5E3%2B2%28-4%29%5E2-11%28-4%29-12+=+-64%2B32%2B44-12=76-76+=+0
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:
x%5E2-2x-3 so you now have:
%28x%2B4%29%28x%5E2-2x-3%29+=+0 Factor the trinomial.
%28x%2B4%29%28x%2B1%29%28x-3%29+=+0 Apply the zero product rule to get:
x+=+-4
x+=+-1
x+=+3
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.
graph%28400%2C400%2C-5%2C5%2C-25%2C15%2Cx%5E3%2B2x%5E2-11x-12%29