Common Core · High school
HSA-APR.B.2
High school — 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).
The skill that covers it
What a student should be able to do
- Divide a polynomial by a linear factor using long or synthetic division, and write the quotient and remainder.
- Use the remainder theorem to evaluate p(k) and the factor theorem to decide whether x - k is a factor.
- Find all the zeros of a factorable polynomial, state each multiplicity, and say whether the graph crosses or touches at each.
- Describe the end behaviour of a polynomial from its degree and leading coefficient, and match a polynomial to its graph.