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.