Question 1108286: Use the Factor Theorem to determine whether the binomial x + 1 is a factor of the polynomial function ƒ(x) = 2x3 – 9x2 + 13x – 6 Answer by ikleyn(52866) (Show Source):
Based on the Factor theorem (whose correct name is the Remainder theorem), your alternative is THIS:
- if (-1) IS the root of the given polynomial, then (x+1) IS the factor;
- if (-1) IS NOT the root of the given polynomial, then (x+1) IS NOT the factor.
And you can easily check it on your own.
------------------ Theorem (the remainder theorem)
1. The remainder of division the polynomial by the binomial is equal to the value of the polynomial.
2. The binomial divides the polynomial if and only if the value of is the root of the polynomial , i.e. .
3. The binomial factors the polynomial if and only if the value of is the root of the polynomial , i.e. .
