So the pair that works is the second pair (x - 3)(6x - 1). For example, f ( x ) x 2 + 5 x + 6 f(x) x2. The last binomial pair has -9x + (-2x) = -11x. Factoring a polynomial is the process of decomposing a polynomial into a product of two or more polynomials. The third binomial pair checks to -3x + (-6x) = -9x. The checking for the first binomial pair is -6x + (-3x) = -9x. This makes only four valid options, total. So if we only need check the binomial pairs that have negative values, we only need to check these factors. Since our original problem has a negative ' b-value,' our possible solutions should be limited to those having negative values within them. EXAMPLE 3 Factoring an Algebraic Expression Factor the expression using the GCF. The original expression shows a total savings of 15. Now we have to piece together all possible binomials: Factoring Polynomials - Key takeaways Factoring a polynomial means is a process of rewriting a polynomial as a product of lower degree polynomials. So, the factored expression shows a 3 discount for every book you buy. Since c = 21, we will factor 21 in as many pairs as possible. In short, we are looking for a pair of numbers that satisfy two requirements at the same time: they must have a product equal to ' c' and a sum equal to ' b.' Use the examples below to help clarify this technique. Then, find the pair that has a sum that amounts to the value of ' b.' When attempting to factor quadratics that have a leading coefficient of 1, we must focus on the values of ' b' and ' c.' The systematic approach for factoring involves factoring ' c' in as many different ways as possible into pairs. Here are the sections in this lesson: Prerequisite Skill: Multiplying Polynomials Motivation for Learning about Factoring Factoring the Greatest Common Factor.

Factoring expressions