Factoring Polynomials 10-2 (page 565 – 571) Distributing and Grouping

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Presentation transcript:

Factoring Polynomials 10-2 (page 565 – 571) Distributing and Grouping By: Julie and Shelby

Warm Up! Find the GCF: Factor each Monomial: 24, 48 3. 44sb2j Review: GCF/GMF (Greatest Common Factor and Greatest Monomial Factor) Find the GCF: Factor each Monomial: 24, 48 3. 44sb2j 16, 72 4. 24c5, 5. 26js4, 16j3, 8j2

Factoring Polynomials: Method 1: Distributing When factoring polynomials use the distributive property backwards Ex: 12mn2 + 18m2n2 Step 1: Factor and find the GCF of the monomials 12mn2= 2 * 2 * 3 * m * n * n 18m2n2= 2 * 3 * 3 * m * m * n * n The GCF = 2 * 3 * m * n * n or 6mn2

Step 2: Now rewrite problem so the GCF will be distributed by dividing it (6mn2) and putting it outside the parentheses and distributing it over whatever is left: 6mn2(2 – 3m) Step 3: Check by redistributing to make sure you come up with the original problem Example 2: 20abc + 15a2c – 5ac Remember: Step One Factor Step Two Distribute Step Three Check 20abc = 15a2c = 5ac =

Practice 1.)12a – 48a2b 2.) 14r2t – 42t = __t(__ - 3)

Factoring Polynomials: Method 2: Grouping The other method of factoring polynomials is grouping, which uses the associative property. This method is used when factoring four or more polynomials. Ex: 12ac + 21ad + 8bc + 14bd Step 1: Apply the associative property (12ac + 21ad) + (8bc + 14 bd)

Step2: Find a common factor between each pair of terms. 12ac + 21ad would have a common factor of 3a. 8bc + 14bd would have a common factor of 2b. Step 3: Factor the first two terms and the last two terms (12ac + 21ad) + (8bc + 14 bd) = 3a(4c + 7d) + 2b(4c + 7d) Because 4c + 7d is a common factor and inside both parentheses, then it can be simplified further. 3a(4c + 7d) + 2b(4c + 7d) = (3a + 2b)(4c + 7d)

Step 4: Check with the FOIL method (3a + 2b) (4c + 7d) = (3a)(4c) + (3a)(7d) + (2b)(4c) +=(2b)(7d)= 12ac 21ad 8bc 14bd Note: If inside the parentheses are not the same, that is as simplified as it will get, but usually they will work out.

Example 2: 20s + 12j = 4(5s + __) Work backwards to solve the problem 20s/4 = 12j/4 = Example 3: (6x2 – 10xy) + (9x – 15y) = 2x(__) + 3(__) *3x - 5y

Practice 1.) 5a – 20 +ac – 4c 2.) 3c – 3 +ac – a

More Practice Express the Polynomials in Factored Form 1.) 9t2 + 36t 2.) 2mk + 7x + 7m + 2xk 3.) 2ax + 6xc + ba + 3bc 4.) 6mn + 15m2