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Complete Guide to Factoring Quadratics and Polynomials

This resource offers a comprehensive overview of factoring techniques, including warm-ups, product finding, and step-by-step factoring examples. Learn how to factor trinomials, recognize common factors, and apply the Add/Multiply Method effectively. Includes practice problems and homework review sections covering a variety of expressions, ensuring a solid understanding of factoring basics. Perfect for students looking to enhance their algebra skills and tackle polynomial expressions confidently.

elizabeth-cochran
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Complete Guide to Factoring Quadratics and Polynomials

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  1. Warm-Up • Find the product • (x+2)(x+6) • (x+7)(x-1) • (x-3)(x-5) • Factor using a GCF • 3x2 -48

  2. Homework Review • 10.8 Worksheet • 1. 3 • 2. 3a2 • 3. 3xy • 4. 5a2b • 5. 5(a2-3) • 6. 7(x+7) • 7. 2y(1+3x) • 8. 8a(x-7) • 9. 12xy(3y-4x) • 10. 15bc3(5b+4c3) • 11. 8(8-5ab) • 12. 9(9-4xy) • 13. t(th+3) • 14. 6(p-12) • 15. 3r(27+16s) • 16. c2(5c-2) • 17. 2e(41e2-61f) • 18. 5q(2-5q) • 19. xy(y+1)

  3. Homework Review • 30. 3c2d3(3c2-2d) • 31. 3y(2+5y) • 32. 5x2y(6x+7y) • 33. ef(6e2-11) • 34. 5rs2(4r2+5s) • 35. 17x2y3(2x2-y2) • 36. 35m2n(m+3n2) • 37. 2d2e2(1-4d4e4) 20. 15cd(1+2cd) 21. a(ab2+1) 22. 3rs(2r-s) 23. l(l-9) 24. 4(d2+4) 25. 6z3(z-3) 26. 4p2(5-4q2) 27. 6(m4-10) 28. 7a2(a+2) 29. 4wv2(4v2+3w2)

  4. Section 10.5 Factoring ax2+bx+c SWBAT to factor trinomials with a=1

  5. Review: Multiply (x + 5)(x + 2) x2 +5x+2x+10 x2+7x+10 x2 5x 2x 10 Notice: 2 and 5 add to get 7 and multiply to get 10

  6. Review: Multiply (x - 3)(x + 4) x2 +4x-3x-12 X2+x-12 x2 4x -3x -12 Notice: -4 and 3 add to get -1 and multiply to get -12

  7. When can you use the Add/Multiply Method? • Do you have a trinomial? • Is a=1?

  8. Steps for the Add/Multiply Method • Step 1: Factor out a GCF if possible • Step 2: Find two numbers that add to get b and multiply to get c • Step 3: Write as a product • Step 4: Check your answer

  9. Example • Factor x2 + 9x + 18

  10. Example • Factor x2 - 4x + 4

  11. Example • Factor 3x2 +3x -18

  12. Example • Factor x2 + 7x + 21

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