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Algebra 1 Unit 3A: Factoring & Solving Quadratic Equations Notes 8 Day 3 – Factor Trinomials with a ≠1 In the previous lesson, we factored polynomials for which the coefficient of the squared term, “a” was always 1. Today we will focus on examples for which a ≠ 1. Looking for Patterns
Finding Factors. Factorizing algebraic expressions is a way of turning a sum of terms into a product of smaller ones. The product is a multiplication of the factors. Sometimes it helps to look at a simpler case before venturing into the abstract.
Example 1. Factor to get Prime Factors. 8x3 − 8. The terms have a common factor, both 8x3 and 8 are divisible by 8. We can rewrite the polynomial as 8(x3 − 1). Can the factors be factored anymore? Let’s repeat the process: (a) There are two terms in x3 − 1. Is it a diference of squares? No, since we have an x3 term. Is it a sum of two cubes?
Factor. Objective: Find the greatest common factor of a polynomial and factor it out of the expression. The inverse of multiplying polynomials together is factoring polynomials. There are many benefits of a polynomial being factored. We use factored polynomials to help us solve equations, learn behaviors of graphs, work with fractions and more.
Trinomials with leading coefficients other than 1 require a different process to factor. We can factor by grouping by taking the middle term and turning it into two terms.
Factoring Quadratic Trinomials Notes. There are several ways we can factor a polynomial of the form ax2 + bx + c, a ≠ 0. Method 1: Reverse FOIL. Mentally work backwards from what we know about FOIL. This works best for the simple case, when a = 1. It is a lot harder when a ≠ 1. List the factors for c. If the sign of c is positive, the signs ...
Objective: Factor trinomials where the coefficient of x2 is one. Factoring with three terms, or trinomials, is the most important type of factoring to be able to master. As factoring is multiplication backwards we will start with a multipication problem and look at how we can reverse the process.
