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Algebra 2 Unit 9 In Class Factoring Practice WS Name: __________________________ Period: __________ This packet includes: factoring notes sample problems of each type FACTORING Two Terms Three Terms More than Three Terms GCF GCF GCF Difference of Perfect Squares Trinomial LC =1 Difference of Perfect Cubes Trinomial LC not =1 Sum of Perfect Cubes Factoring Notes 1) 2) 3) 4) 5) 6) 7) 8) Take out the greatest common factor (reverse distributive property) Difference of perfect squares Sum of perfect cubes Difference of perfect cubes Perfect square trinomial Trinomial with leading coefficient of 1 Trinomial with leading coefficient not equal to 1 Grouping Grouping ALWAYS FIRST look for a GCF in all terms. If there is, pull out the GCF in front. In the parenthesis goes what’s left over. Ex: 15xy2 – 10 x3y + 25 xy3 = 5xy( 3y – 2x2 + 5y2) IF THERE ARE 2 TERMS: it could be….. Difference of perfect squares: Your answer is the product of two binomials. Take the square root of each term. One binomial is Plus and the other binomial is Subtract. Ex: 4x2 – 25y4 = (2x + 5y2)(2x – 5y2) Sum or Difference of a perfect cube: Your answer is a binomial times a trinomial. Binomial part is the cube root of each original term with the same sign. For the Trinomial part only look at the new binomial (not the original problem and use SOFAS). Square the first term, Opposite sign, multiply the First term by the second term, Always positive, Square the second term. Ex: 8x3 – y3 = (2x – y)(4x2 + 2xy + y2) IF THERE ARE 3 TERMS: it could be….. Perfect square trinomial if the first and last terms are perfect squares and the middle term is twice the product of the square root of the first and last. Find numbers that multiply to = -12 and add to = -4. The numbers are –6 and + 2. Ex: x2 + 6x + 9 = (x + 3)2 and A trinomial with leading coefficient of 1. You must find two numbers that multiply to equal the last term add to equal the middle term. Your answer is the product of two binomials. Ex: x2 – 4x – 12 = (x + 2)(x – 6) A trinomial with leading coefficient not equal to 1. Your answer will be the product of two binomials. There are a few different methods that teachers often use. “The Magic Box”, “T-chart”, guess and check. I will do the divide, reduce and swing method here. Ex: 3x2 + 10x + 8 (x + 6)(x + 4) * Two numbers that multiply to be 24 and add to be 10 are 6 and 4. * Use these two numbers with correct sign and write as binomials 6 4 ( x )( x ) 3 3 4 ( x 2)( x 3) * Divide the plain numbers (6 and 4) by the leading coefficient (3). (3x + 4)(x + 2) * Swing the denominator of any unreduced fraction up to the front of that binomial. * Reduce the fraction if possible. IF THERE ARE 4 TERMS: Grouping. Group two terms together and another two terms together leaving an addition sign in between the two binomials. Take out a GCF from each binomial. Your goal is that inside the parenthesis are identical. If this happens then you rewrite your answer as the product of two binomials. Ex: 12ac + 21ad + 8bc +14bd Step 1. (12ac + 21ad) + (8bc + 14bd) Step 2. 3a(4c + 7d) + 2b(4c + 7d) Step 3. (3a + 2b)(4c + 7d) Use the attached “factoring notes” to brush up on your factoring skills. Factor completely. EXPRESSION FACTORED FORM TYPE 1. 16m2n + 12mn2 GCF 2. x2 – 2x GCF 3. x2 – 25 Diff. of Perfect Sq’s 4. x4 – 1 Diff. of Perfect Sq’s (twice) 5. 3a2 – 27b2 Combo: GCF & Per. Sq’s 6. x3 + 125 Sum of Perfect Cubes 7. a3 – b6 Diff. of Perfect Cubes 8. x3 + 27 Sum of Perfect Cubes 9. x2 + 8x + 16 Perfect Square Trinomial 10. 2t3 + 32t2 + 128t Combo: GCF & Trinomial 11. a 3b 3 c 6 Diff. of Perfect Cubes WORK 12. 4w 2 12wr 9r 2 Perfect Sq. Trinomial 13. 8x3 y 3 Sum of Perfect Cubes 14. 20 x 2 60 x 35 Combo: GCF & Trinomial 200 17 r r 2 15. Trinomial DO NOT SWITCH THE ORDER! 16. 17. 18. 6x2 + 10x – 4 Combo: GCF & Trinomial 4 x 2 8 x 4 xy 8 y Combo: GCF & Grouping 21 – xy – 7y + 3x Grouping