<p> MAC 1140 – Review Factoring Trinomials COMPLETELY</p><p>REVIEW MULTIPLYING: Multiply using FOIL: 1. (x – 3)(x – 5) 2. (x + 3)(x + 5) 3. (x – 3)(x + 5) </p><p>4. (3x + 2)(2x –1) 5. (5x + 2y)(2x – 3y) 6. (x + y)(x – y)</p><p>Ia. FACTOR: If the polynomial is a trinomial, ax2 + bx + c, and a=1, use FOIL backwards-Trial and Error. Check using FOIL.</p><p>1. x2 – 5x + 6 2. x2 + 2x - 18 3. x2 – 7xy – 18y2</p><p>1b. FACTOR: If the polynomial is a trinomial, ax2 + bx + c, and a  1, use FOIL backwards or the “ac” method. In the “ac” method, look for a pair of terms such that their product = ac and their sum = b. Replace bx with the sum of the two terms. Then factor using grouping. Check using FOIL. 4. 3x2 - 13x + 4 5. 2x2 + x - 6 6. 6x2 - 7xy + 2y2</p><p>STRATEGY FOR FACTORING COMPLETELY A. FIRST: Always look for greatest common factor !! Ask: Can I take anything out?</p><p>B. 2 TERMS Difference of squares? x2 – y2 = (x+y)(x-y) (Remember: x2 + y2 does not factor.) (may factor again: x4 – 16 for example becomes (x 2 - 4)(x2 + 4) which factors again to become (x - 2)(x + 2)(x2 + 4) Difference of cubes? F3 - L3 = (F - L)(F2 + FL + L2) Sum of cubes:? F3 + L3 = (F + L)(F2 - FL + L2)</p><p>Examples of Factoring Cubes: 27x3-125 = (3x)3-53= x3 + 8 = x3 + 23 = (x + 2) (x2 - x2 + 22) = (3x - 5) ((3x)2 + (3x)(5) + 52) = (x + 2) (x2 - 2x + 4) = (3x - 5) ( 9x2 + 15x + 25)</p><p>C. 3 TERMS Factor using FOIL backwards (Trial and Error) or “ac” method.</p><p>D. 4 Terms: Try to factor by grouping first two and then last two terms. Factor the following.</p><p>1. x2 + 3x – 18 2. 3x2 – 9x – 12 3. 3x2 + 11x + 6</p><p>4. 18x2 + 3x – 15 5. 3x3 + 24 6. 5x4 – 5y4 (See Back)</p><p>Homework </p><p>Factor completely and check using FOIL:</p><p>1. 2x2 - 128 2. 20x3 - 4x2 - 72x</p><p>3. 2x2 - 11x + 12 4. 1 - y3</p><p>5. 8x5 + 64x2 6. 3t2 - 27</p><p>7. 3a2 - 30a + 75 8. 8y2 - 18y - 5</p><p>9. x3 + 24x2 + 144x 10. 4x4 - 64</p><p>11. x5 - 4x4 + 7x3 12. 24x2 + 10x - 4</p><p>13. 35x2 + 34x + 8 14. 25x2 +10xy + y2</p><p>15. 30x2 - 33x - 18 16. 18x2 - 3x - 10 Answers to Worksheet Homework- Review </p><p>1. 2(x+8)(x-8) 2. 4x(5x+9)(x-2) 3. (2x-3)(x-4)</p><p>4. (1-y)(1+y+y2) 5. 8x2(x+2)(x2-2x+4) 6. 3(t+3)(t-3)</p><p>7. 3(a-5)(a-5) or 8. (4y+1)(2y-5) 9. x(x+12)(x+12) or 3(a-5)2 x(x+12)2</p><p>10. 4(x2+4)(x+2)(x-2) 11. x3(x2-4x+7) 12. 2(3x+2)(4x-1)</p><p>13. (5x+2)(7x+4) 14. (5x+y)(5x+y) 15. 3(5x+2)(2x-3)</p><p>16. (6x-5)(3x+2)</p>