Question

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.

Answer 1

Answer:

Remainder= 5, and the binomial $(x-1)$ is not a factor of the given polynomial.

Step-by-step explanation:

Given polynomial is $(2x^3-3x^2+6)$ , we have to divide this with a binomial [tex}(x-1)[/tex] using remainder theorem.

Remainder theorem says if $(x-a)$ is a factor then remiander would be $f(a)$

Therefore for $(x-1), \ {we find}\ f(1)}$

$f(1)=(2\times 1^3-3\times1^2+6)\\1^3 =1\\1^2=1\\Substituting \ this \ above\\f(1)= (2-3+6)=5$

Thus the remainder is 5 and since it is not 0 , so the binomial $(x-1)$ is not a factor of the given polynomial.

Answer 2

Answer:

Remainder= 0 and it is a polynomial

Step-by-step explanation:

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