Define factor theorem.

Understand the Problem

The question is asking for a definition of the Factor Theorem, which is a fundamental concept in algebra and polynomial functions. It states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0, meaning that c is a root of the polynomial.

Answer

For a polynomial p(x), x-a is a factor if and only if p(a) = 0.

The Factor Theorem states that for a polynomial p(x), x-a is a factor of p(x) if and only if p(a) = 0.

Answer for screen readers

The Factor Theorem states that for a polynomial p(x), x-a is a factor of p(x) if and only if p(a) = 0.

More Information

The Factor Theorem connects the roots or zeros of a polynomial to its factors, aiding in polynomial factorization.

Tips

A common mistake is assuming p(a) = 0 implies x+a is a factor, rather it's x-a.

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