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Precalculus - Polynomial and Rational Functions

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Study GuidePrecalculus–Polynomial and Rational Functions1. Factoring PolynomialsFactoring is likeundoing multiplication.Instead of multiplying expressions together, you break a polynomial into simpler parts whose productgives you the original expression.Factoring is one of the most important skills in algebra. It helps you:•Solve higher-degree equations•Simplify expressions•Understand how polynomials are builtYou may already know some factoring, but this chapter reviews the key methods you should becomfortable with.1. Greatest Common Factor (GCF)Thegreatest common factoris the largest factor that dividesevery termin a polynomial evenly.If all terms share one or more common factors, you can factor them out just like you would factornumbers.How to find the GCF:1.Look at the numbers in each term.2.Look at the variables and take the smallest power they all share.3.Multiply those together.Example 1:Factor the expressions(a)Each term is divisible by5andx, so the GCF is5x.

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Study GuideFactor it out:(b)The largest factor shared by all terms is:Factor it out:2. Factoring by GroupingSometimes, the greatest common factor isnot just a number or variable, but an entire expression inparentheses.In these cases, you:1.Group terms together.2.Factor each group.3.Look for a common binomial factor.Example 2:Factor the expressions(a)Every term contains ((x-5)).Factor it out:

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Study Guide(b)There is no single GCF for all four terms, so group them:Factor each group:Now factor out ((x-2)):3. Factoring Quadratic TrinomialsOne of the most common factoring tasks is rewriting aquadratic trinomialas the product of twobinomials.When the leading coefficient is 1Use this method when the expression looks like:Findtwo numbersthat:•Add up to the middle coefficient•Multiply to the constant termExample 3(a)

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Study GuideWe need two numbers that:•Add to (-4)•Multiply to (-12)Those numbers are (-6) and (2).So the factorization is:(b)The numbers that add to (-10) and multiply to (24) are (-6) and (-4).So:When the leading coefficient is not 1Now the expression looks like:You still look for two numbers that:•Add to the middle coefficient•Multiply to (a\times c)Then rewrite the middle term and factor by grouping.(c)Multiply the leading coefficient and constant:
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Document Details

University
Texas A&M University
Course
Precalculus
Subject
Mathematics

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