Common Core · High school
HSF-IF.C.7.C
High school — Graph polynomial functions, identifying zeros when suitable factorisations are available, and showing end behaviour.
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.