Question

Use the remainder theorem to find the remainder of 2x^4 + x^2 - 10x -1 divided by x +2.

Answer 1

Remainder Theorem says that if there is any Polynomial equation P(x), which is to be divided by (x - a) then remainder can be calculated by substituting value of a in equation P(x).  

$2x^{4} +x^{2}-10x-1$ = P(x)   divided by   $(x+2)$

Step 1: Find a

To find a we will have to convert (x+2) into (x - a) form

i.e.  (x+2) = (x - (-2))

therefore, a = -2

Step 2: Substitute value of a in P(x),

By substitution we get,

$2(-2)^{4}+(-2)^{2}-10(-2)-1$

= $2(16) + 4 +20 -1$

= $32 +4 + 20 - 1$

= $55$ = Remainder

Hence, Remainder is 55.