Factor theorem

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Solution

The Factor Theorem is a result of the Remainder Theorem, and is based on the same reasoning. If you haven't read the lesson on the Remainder Theorem

As the Remainder Theorem points out, if you divide a polynomial p(x) by a factor x – a of that polynomial, then you will get a zero remainder. Let's look again at that Division Algorithm expression of the polynomial:

p(x) = (x – a)q(x) + r(x)

If x – a is indeed a factor of p(x), then the remainder after division by x – a will be zero. That is:

p(x) = (x – a)q(x)

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Similar questions

What's the difference between remainder theorem and factor theorem?

Factor Theorem is equivalent to Remainder Theorem when remainder is

Factor Theorem is equivalent to Remainder Theorem with remainder $0$ .

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