A-APR.2.2

Know 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).

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The purpose of this task is to emphasize the use of the Remainder Theorem (a discussion of which should obviously be considered as a prerequisite for the task) as a method for determining structure in polynomial in equations, and in this particular instance, as a replacement for division of polynomials.
The Missing Coefficient
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This task continues ''Zeroes and factorization of a quadratic polynomial I.''
Zeroes and factorization of a quadratic polynomial II
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For a polynomial function p, a real number r is a root of p if and only if p(x) is evenly divisible by x−r. This fact leads to one of the important properties of polynomial functions: a polynomial of degree d can have at most d roots.
Zeroes and factorization of a quadratic polynomial I
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For a polynomial function f, if f(0)=0 then the polynomial f(x) is divisible by x. This fact is shown and then generalized in ''Zeroes of a quadratic polynomial I, II'' and ''Zeroes of a general polynomial.''
Zeroes and factorization of a non polynomial function
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This task builds on ''Zeroes and factorization of a quadratic function'' parts I and II.
Zeroes and factorization of a general polynomial
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The task has students use the remainder theorem to deduce a linear factor of a cubic polynomial, and then to completely factor the polynomial.
Graphing from Factors III