Algebra — Factorizing by Taking Out Greatest Common Factor GCF

About this lesson

This unit teaches factorization of polynomials by taking out the greatest common factor (GCF). It begins by defining polynomials, monomials, binomials, and trinomials, and then explains the steps to factorize a polynomial: factor each term into primes and variables, identify the GCF, divide the polynomial by the GCF, and write the result as the GCF times the quotient. Examples include factorizing expressions like 6x^2 - 15x and 8x^2 - 16. The unit also covers factorizing expressions where the common factor is a binomial, such as (x+y) or (x-5), and emphasizes taking -1 as a common factor when the leading coefficient is negative. It introduces the concept of a prime polynomial that cannot be factorized. Students learn to use factorization to find numerical values of expressions (e.g., 19×23 + 19×27) and to solve quadratic equations like 3x^2 + 6x = 0 by setting each factor to zero. The unit includes self-evaluation exercises, examples, and a variety of practice problems, including word problems from geometry, engineering, aquatic life, and industry. By the end, students should be able to factorize polynomials by taking out the GCF, use this to simplify expressions and solve equations, and apply it to real-world contexts.