SOLUTION: PLEASE HELP!!!! use synthetic division and the Factor Theorem to determine whether the given binomial is a factor of P(x). P(x)=x^3+2x^2-5x-6, x-2

Question 1051087: PLEASE HELP!!!!
use synthetic division and the Factor
Theorem to determine whether the given binomial is a
factor of P(x).
P(x)=x^3+2x^2-5x-6, x-2

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
change the sign of the -2 to 2 and divide
2/1===+2====-5====-6
==1=(2)=4=(8)=3==(6)0, the parentheses are the intermediate products which are added to the coefficients. You multiply each result by +2 and add.
Because the remainder is 0, it factored.
What is left is a 1===4====3
These are coefficients of a polynomial to one less power, here x^2+4x+3
That happens to factor as well (x+3)(x+1), but that isn't required to be answered here. The polynomial factors completely, and x-2 is a factor, and x=2 is the root.
How do you remember whether to change the sign?
Use a polynomial you know, like x^2-6x+9 where the factors are (x-3)^2
The roots are x=3
If you use 3, you get a remainder of 0.
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