Quadratics and Polynomials: Free Course

About this course

Polynomial structure makes expansion and factoring connected operations. This course develops polynomial arithmetic, common factors, special products and quadratic equations solved by factoring. Study the complete public source playlist from Khan Academy in English, with all 24 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Add, subtract and multiply polynomials.
• Recognize common factors and special products.
• Factor selected quadratic and higher-degree expressions.
• Use factored forms to solve equations and dimension problems.

Skills you’ll gain

• Polynomial arithmetic
• Factoring
• Special products
• Quadratic equations

Course Overview

The recordings identify terms and coefficients before working with sums, differences and products. Binomial multiplication leads to squares and differences of squares, while common factors and grouping provide routes in the opposite direction. Quadratic examples connect a factored expression with the solutions of an equation. Geometry applications use area or volume to interpret factors as dimensions, reminding learners to apply any restrictions imposed by the context. The course is a focused polynomial-and-factoring sequence; it should not be mistaken for a complete treatment of every method for solving quadratics. Verify a factorization by multiplication rather than relying only on its appearance.

How to study the course

• Videos 1–6: this part of the source list includes “Factoring quadratics as (x+a)(x+b) (example 2)” through “Example 1: Factoring trinomials with a common factor”. State the quantities and conditions before calculating. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 7–12: this part of the source list includes “Example 4: Factor a polynomial with two variables by taking a common factor” through “More examples of addition and subtraction of polynomials”. Keep equivalent expressions or representations connected. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 13–18: this part of the source list includes “Example 3: Factor a quartic binomial with two variables by taking a common factor” through “Example 1: Multiplying binomials to get a difference of squares”. Check each operation with a small example before extending it. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 19–24: this part of the source list includes “Example 1: Factor a linear binomial by taking a common factor” through “Multiplying binomials with radicals”. Explain a result in words as well as symbols. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits students, returning learners and anyone strengthening the specific mathematics named in the course. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort with the preceding arithmetic or algebra skills is useful. Keep paper, a pencil and a calculator when a lesson uses one. Grade-specific courses assume the learner’s earlier grade-level knowledge.

Put the lessons into practice

Expand a product of two binomials and then recover its factors. Compare a perfect-square expression with a difference of squares. Solve a quadratic by factoring and check each solution in the original equation. Add an area or volume context and explain which algebraic solutions are meaningful dimensions.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.