Question

On dividing polynomial p(x) by a linear binomial, X - a, we get a quotien

statements must be proven true for the remainder theorem to be true

Answer 1

Explanation:

Hello, we can write

(1) p(x)=(x-a)q(x)+r

`\boxed{\sf v}` True

It means that p(a)=0 * q(a) + r = r

so the first one is true.

`\boxed{}` False

The second one is not to be proven true from the remainder theorem.

`\boxed{\sf v}` True

For x different from a we can divide the equation (1) by (x-a).

`\boxed{}` False

We cannot say anything on q(a).

`\boxed{\sf v}` True

If the rest is 0 then it means that p(a) = 0

`\boxed{\sf v}` True

If p(a) = 0 it means that the rest r = 0 and then p(x)=q(x)(x-a)

Thank you