MA19.PRE.16

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.16
Derive and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

Unpacked Content

Knowledge

Students know:

Procedures for dividing a polynomial p(x) by a linear polynomial (x - a).

Skills

Students are able to:

Accurately perform procedures for dividing a polynomial p(x) by a linear polynomial (x - a),
Evaluate a polynomial p(x) for any value of x.

Understanding

Students understand that:

There is a structural relationship between the value of a in (x - a), as well as the remainder when p(x) is divided by (x - a).
If p(a)=0, then x-a if a factor of p(x).

Vocabulary

If and only if
Remainder theorem

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