Common Core · High school
HSA-APR.D.6
High school — Rewrite simple rational expressions in different forms: write a(x)/b(x) in the form q(x) + r(x)/b(x), where the degree of r(x) is less than the degree of b(x), using inspection or long division.
The 2 skills that cover it
- Polynomial FunctionsDivide one polynomial by another, use the remainder and factor theorems to find zeros, and read the end behaviour and shape of a polynomial graph from its degree and leading coefficient.Read the lesson →
- Rational Expressions & EquationsTreat a fraction of polynomials the way you treat a fraction of numbers: simplify it by factoring, state the values it excludes, multiply, divide, add and subtract, and solve equations that contain one.Read the lesson →
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.
- Simplify a rational expression by factoring, and state the values of the variable that are excluded.
- Multiply and divide rational expressions, cancelling common factors.
- Add and subtract rational expressions using a least common denominator.
- Solve a rational equation by clearing denominators, and reject any solution that makes a denominator zero.