SOLUTION: Prove that the following binomial is one of the factors of the second polynomial: Binomial: a+2 Polynomial: a^4+3a^3-a^2-a+10

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Prove that the following binomial is one of the factors of the second polynomial: Binomial: a+2 Polynomial: a^4+3a^3-a^2-a+10      Log On


   

Question 870616: Prove that the following binomial is one of the factors of the second polynomial:
Binomial: a+2
Polynomial: a^4+3a^3-a^2-a+10
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Quotient of polynomial divided by binomial must have remainder of zero.

Using synthetic division:

_________|_____1______3______-1______-1________10
_________|
____-2___|___________-2______-2_______6________-10
_______________1______1______-3_______5________0 .


Notice that remainder is zero. a+2 is a factor of the polynomial.