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(Remainder Theorem).

When a $(x)$ is divided by $x-k$ the remainder is $a(k)$.

Proof.

The remainder theorem allows us easily to find factors of a polynomial.

Remember that a factor of a polynomial divides exactly into the polynomial i.e. has a remainder of $0 .$

So if we can find a value $k$ which when substituted into the polynomial gives a value of 0 we know by the Remainder Theorem that this value is the remainder when dividing by $(x-k)$ so if the value is 0 we know $(x-k))$ is a factor.

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