Algebra — Factorizing by Grouping

About this lesson

This unit teaches algebraic factorization by grouping, including methods for four-term polynomials and trinomials, as well as completing the square to factorize and solve equations. It covers two grouping methods: grouping into binomials to find a common factor, and grouping into a perfect square trinomial with a fourth square term to use difference of squares. Completing the square is introduced as adding a term to make a perfect square trinomial, with applications to factorizing expressions and solving quadratic equations. Real-life problems include determining dimensions of a library plot, a cuboid glass box, storage units, and a framed picture. The unit includes worked examples, self-evaluations, exercises, and a unit assessment. By the end, students should be able to factorize polynomials by grouping, complete the square, solve equations using these techniques, and apply them to geometric and practical problems.