Presentation on theme: "5-4 Factoring Polynomials"— Presentation transcript:
1 5-4 Factoring Polynomials Objectives:Students will be able to:Factor polynomialsSimplify polynomial quotients by factoring
2 FactoringThere are various different techniques used to factor polynomials.The technique(s) used depend on the number of terms in the polynomial, and what those terms are.Throughout this section we will examine different factoring techniques and how to utilize one or more of those techniques to factor a polynomial.
3 What is a GCFGreatest common factor (GCF): largest factor that all terms have in commonYou can find the GCF for a polynomial of two or more terms.
4 Example 1: Finding a GCFExample 1: Find the GCF of each set of monomials.8, 12 b) 10, 21 c) 24, 60, 364112
9 GroupingGrouping is a factoring technique used when a polynomial contains four or more terms.
10 Steps for Factoring By Grouping Group terms with common factors (separate the polynomial expression into the sum of two separate expressions)Factor the GCF out of each expressionRewrite the expression using the distributive property (factor into a binomial multiplied by a binomial)
15 Factoring Trinomials The standard form for a trinomial is: The goal of factoring a trinomial is to factor it into two binomials. [If we re-multiplied the binomials together, that should get us back to the original trinomial.]
16 Steps to factor a Trinomial Steps for factoring a trinomialMultiply a * c2) Look for factors of the product in step 1 that add to give you the ‘b’ term.3) Rewrite the ‘b’ term using these two factors.4) Factor by grouping.
28 Additional Factoring Techniques There are certain binomials that are factorable, but cannot be factored using any of the previous factoring techniques.These binomials deal with perfect square factors or perfect cube factors.
40 Simplifying Polynomial Quotients In the previous section (5-3), we learned to simplify the quotient of two polynomials using long division or synthetic division. Some quotients can be simplified using factoring. To do so: 1) factor the numerator (if possible) 2) factor the denominator (if possible) 3) reduce the fraction TIP: Be sure to check for values that the variable cannot equal. Remember that the denominator of a fraction can never be zero.
41 Ex1: Simplify Factor Numerator and Denominator! Eliminate Common Factors in Numerator and Denominator!