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).
[tex]2x^{4} +x^{2}-10x-1[/tex] = P(x) divided by [tex](x+2)[/tex]
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,
[tex]2(-2)^{4}+(-2)^{2}-10(-2)-1[/tex]
= [tex]2(16) + 4 +20 -1[/tex]
= [tex]32 +4 + 20 - 1[/tex]
= [tex]55[/tex] = Remainder
Hence, Remainder is 55.
