Question 982436


The &nbsp;<B>Factor Theorem</B>&nbsp; says &nbsp;(see the &nbsp;<A HREF=https://en.wikipedia.org/wiki/Factor_theorem>article</A>&nbsp; in &nbsp;<B>Wikipedia</B>, &nbsp;or the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Divisibility-of-polynomial-f%28x%29-by-binomial-x-a.lesson>Divisibility of polynomial f(x) by binomial x-a</A>&nbsp; in this site, &nbsp;or the lesson &nbsp;<A HREF=http://www.purplemath.com/modules/factrthm.htm>The Factor Theorem</A>&nbsp; from the other site):<BLOCKQUOTE>If a polynomial &nbsp;f(x)&nbsp; has the number &nbsp;x = a&nbsp; as the root, &nbsp;i.e. &nbsp;f(a) = 0, &nbsp;then the polynomial &nbsp;f(x)&nbsp; has the binomial &nbsp;x-a&nbsp; as the factor. &nbsp;In other words, &nbsp;the binomial &nbsp;x-a&nbsp;  divides &nbsp;f(x)&nbsp; without a remainder.</BLOCKQUOTE>In your case, &nbsp;in order to prove that &nbsp;{{{x^8 + 2x^7 + x + 2}}}&nbsp; has the binomial &nbsp;x+2&nbsp; as the factor, &nbsp;you simply should to check that the number &nbsp;-2&nbsp; is the root of this polynomial. &nbsp;It is easy to do. &nbsp;Simply substitute the number &nbsp;-2&nbsp; into the polynomial and calculate the result. 


Please do it yourself.