Use the Remainder Theorem to find the remainder for (2x^3-3x^2+6)/(x-1) and state whether or not the binomial is a factor of the polynomial.
Accepted Solution
A:
Answer:Remainder= 5, and the binomial [tex](x-1)[/tex] is not a factor of the given polynomial.Step-by-step explanation:Given polynomial is [tex](2x^3-3x^2+6)[/tex] , we have to divide this with a binomial [tex}(x-1)[/tex] using remainder theorem.Remainder theorem says if [tex](x-a)[/tex] is a factor then remiander would be [tex]f(a)[/tex]Therefore for [tex](x-1), \ {we find}\ f(1)}[/tex][tex]f(1)=(2\times 1^3-3\times1^2+6)\\1^3 =1\\1^2=1\\Substituting \ this \ above\\f(1)= (2-3+6)=5[/tex]Thus the remainder is 5 and since it is not 0 , so the binomial [tex](x-1)[/tex] is not a factor of the given polynomial.