Polynomials and Factoring

What this unit covers

The resources here follow polynomials from first definitions through to factoring and theorems. The quiz Classifying Polynomials asks you to spot monomials, binomials and trinomials and to state the degree. The Algebra II First Nine Weeks Exam Test goes on to simplifying and adding polynomials. Further along you will find division, binomial expansion, roots, rational expressions and partial fractions.

Where to start

If the vocabulary is new, begin with Classifying Polynomials. Then move to the quiz Adding & Subtracting Polynomials and the flashcards Adding and Subtracting Polynomials (Section 6.4), which let you repeat the same card until the method sticks.

Once that feels steady, turn to factoring. A sensible order is:

1. The mind map Steps for factoring quadratic expressions, which starts with finding the greatest common factor.
2. The quiz Factoring Quadratics, where you factor expressions and judge true or false statements.
3. The Pre-Test on Factoring Trinomials, to check what you can do without help.
4. The quiz Dividing Polynomials, which leads towards the theorems.

Using maps and quizzes together

Read a mind map first to see the whole method on one screen. The Polynomials mind map sets out the factor theorem: if (x-a) is a factor of f(x), then f(a)=0. It also gives the remainder theorem, where f(a) is the remainder when f(x) is divided by (x-a). After reading, take a quiz and note which questions slow you down. Go back to the map for only those steps, then try the quiz again.

For exam-style practice, the slide set Factor Theorem and Remainder Theorem exam questions is a useful next step, and the mind map How to Determine the End Behaviour of a Polynomial Function covers the shape of curves.

Where it sits

This unit belongs to the Algebra strand of Mathematics. Most of the material is aimed at school students, and teachers can use the quizzes and flashcards as ready-made starters or revision tasks. Everything was made by GoConqr users, so styles and notation vary a little from one resource to the next.

Choose one resource that matches where you are now, work through it, then move on to the next step in the list above.