SOLUTION: Use synthetic division and the Factor Theorem to determine whether (x + 1/2) is a factor of P(x) = 10x^4 + 9x^3 – 4x^2 + 9x +6.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use synthetic division and the Factor Theorem to determine whether (x + 1/2) is a factor of P(x) = 10x^4 + 9x^3 – 4x^2 + 9x +6.       Log On


   

Question 260983: Use synthetic division and the Factor Theorem to determine whether (x + 1/2) is a factor of P(x) = 10x^4 + 9x^3 – 4x^2 + 9x +6.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
(I'm going to use 0.5 instead of 1/2 to make things easier for me.)
(x+0.5) is a factor of a polynomial if it divides evenly (IOW the remainder is zero) into the polynomial. So all we have to do is divide the polynomial by (x+0.5) and see if the remainder is zero:
-0.5 |   10    9   -4   9   6
------        -5   -2   3  -6
         ---------------------
         10    4   -6  12   0

The remainder is 0. So (x + 0.5) is a factor of P(x). (The other factor, taken from the numbers in front of the remainder, is 10x%5E3+%2B4x%5E2+-6x+%2B12