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• FACTORING EXPRESSIONS HOW TO

Is important to note that not all quadratics of this form can be factored, so the process we This suggests a process we can follow to work in the opposite direction andįactor an expanded quadratic of the form 𝑥 + 𝑏 𝑥 + 𝑐  into the product of two

Our solution, the 𝑥-term is written as the sum of two terms with these coefficients Sum of the constant terms in the two binomials ( 8 = 3 + 5 ) and in the penultimate line of The coefficient of 𝑥 in the trinomial is the We can observe that the constant term in the trinomial expression is the product of theĬonstant terms in the two binomials ( 1 5 = 3 × 5 ). ĭistributing each set of parentheses and collecting like terms gives We begin by distributing the first set of Consider the expansion of the product of the binomials Factoring is the reverse process of distributing parentheses, orĮxpanding brackets.

FACTORING EXPRESSIONS HOW TO

We now consider how to factor a quadratic expression of the form

This expression cannot be factored any further, as the two terms in each In the first part of theīinomial is multiplied by 𝑥, and in the second part, it is multiplied by 2. We can, therefore, factor by this shared binomial. Upon inspection, we observe that the two parts of this expression share a That is already in a partially factored form.Įxample 1: Factoring an Expression with a Common Binomial Term We first demonstrate the process of factoring an expression with a common binomial term Each of the examples we consider here are of this type. The same algebraic structure, then we are be able to combine one pair of like terms, leading Multiplying each term in one binomial by each term in the other.

In general, when we multiply two binomials, we initially obtain four terms, created by The same principle is true when we factor algebraicĮxpressions the focus of this explainer is writing trinomials as the product of two binomial When we list the factors of a number, we can write the number as a product of its factors. Definitions: Monomial, Binomial, and TrinomialĪ monomial is a product of numbers and powers of variables.Ī binomial expression is the sum or difference of two monomials.Ī trinomial expression is the sum or difference of three monomials.Īn example of a monomial expression is − 5 𝑥 𝑦 .Īn example of a binomial expression is 3 𝑥 + 7 .Īn example of a trinomial expression is 2 𝑎 − 2 𝑎 𝑏 + 3 𝑏 .