SOLUTION: Use the Factor Theorem to determine whether the first polynomial is a factor of the second. x + 2; x^8 + 2x^7 + x + 2

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Question 982436: Use the Factor Theorem to determine whether the first polynomial is a factor of the second.
x + 2; x^8 + 2x^7 + x + 2
Answer by ikleyn(52864)   (Show Source): You can put this solution on YOUR website!

The  Factor Theorem  says  (see the  article  in  Wikipedia,  or the lesson  Divisibility of polynomial f(x) by binomial x-a  in this site,  or the lesson  The Factor Theorem  from the other site):
If a polynomial  f(x)  has the number  x = a  as the root,  i.e.  f(a) = 0,  then the polynomial  f(x)  has the binomial  x-a  as the factor.  In other words,  the binomial  x-a  divides  f(x)  without a remainder.
In your case,  in order to prove that    has the binomial  x+2  as the factor,  you simply should to check that the number  -2  is the root of this polynomial.  It is easy to do.  Simply substitute the number  -2  into the polynomial and calculate the result.

Please do it yourself.


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