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Polynomial Multiplication Exercises and Factoring Techniques

Practice multiplying polynomials and learn various factoring methods including GCF, trinomials, grouping, squares, and cubes. Prepare for the upcoming quiz in Section P5.

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Polynomial Multiplication Exercises and Factoring Techniques

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  1. Warm-Up #2 Multiply these polynomials. (x-5)2 (8x-1)2 3. (4x- 3y)(3x +4y) Homework: P5 (1,3,5,11,13,17,27,33,41, 45,49,55,59,63,71,73,77) Answers: x2 – 10x + 25 64x2 – 16x + 1 12x2y2 + 7xy - 12y2

  2. Daily Question What are at least 3 ways to factor polynomials?

  3. Announcements: Section P5:Factoring Polynomials • Factoring GCF, • Trinomials, • By grouping, • Difference of Two Squares • Sum or Difference of a cube Quiz P4/P5 on 7/26!!!

  4. Factoring GCF • Ex1: 16x – 24 • Ex 2: 6x4 -12x3 + 12x2 8(2x – 3) 6x2(x2 – 2x + 2) YOU TRY: 12x5 – 8x4 + 4x2 4x2(3x3 – 2x2 + 1)

  5. Ex 3: x2+12x +36 (x +6)(x+6) (x+6)2 Ex. 4: 25x2-60x + 36 (5x-6) (5x-6) (5x-6)2 Factoring Perfect Trinomials • * (a+b)2or (a-b)2

  6. Factoring Trinomials – Don’t forget GCF! • x2 + x - 12 • 2x2 – 11x – 6 • 6x2 + 14x + 8 • (x + 4)(x – 3) • (2x + 1)(x – 6) • 2(3x + 4)(x+1)

  7. YOU TRY: • 3x2 -2x -5 • 6x2-18x-60 (3x-5)(x+1) 6(x-5)(x+2)

  8. Factoring by Grouping • Ex. 5: x3 - 2x2 + 5x -10 • Ex. 6: x3 - 3x2 + 4x -12 (x-2)(x2+5) (x-3)(x2+4) YOU TRY: 3x3 - 2x2 - 6x + 4 (3x-2)(x2-2)

  9. Ex. 7: x2-4* Remember to take the square root of the 1st term and the last term. One factor is positive and one factor is negative. (x+2)(x-2) Ex.8: 81x2- 49 Factoring the Difference of Two Squares (9x-7)(9x+7)

  10. YOU TRY: (6x-7y)(6x+7y) 36x2-49y2

  11. Factoring the Sum and Difference of Cubes: Don’t forget to check for the GCF!! Formulas: SUM: A3 + B3 = (A + B)(A2 – AB + B2) DIFFERENCE: A3 - B3 = (A-B)(A2 + AB + B2) A and B come from cube rooting the terms in the problem.

  12. Example 9: x3 + 8 Step 1: Check for GCF, there is none Step 2: Cube root terms A = x and B = 2 Step 3: Follow formula A3 + B3 = (A + B)(A2 – AB + B2) = (x+ 2)(x2 - 2x + 4)

  13. Example 10: b) 64x3 -125 Step 1: Check for GCF, there is none Step 2: Cube root terms A = 4x and B = 5 Step 3: Follow formula A3 - B3 = (A - B)(A2 + AB + B2) = (4x - 5)(16x2 + 20x + 25)

  14. YOU TRY!!! Answers: (x+4)(x2 – 4x + 16) (5x – 2)(25x2 + 10x + 4) x3 + 64 b) 125x3 – 8

  15. Summary: Which type of factoring a polynomial do you like the best and why? Which type of factoring a polynomial do you think is the hardest for you and why?

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