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Factoring Part 3

Factoring Part 3. Wednesday, April 2 nd. Homework check!. Factoring Warm-Up. In your teams, factor the following: . 16x 4 – 20x 3. Factoring Warm-Up. In your teams, factor the following: . x 2 – 12x + 20. Factoring Warm-Up. In your teams, factor the following: . 2x 2 – 10x – 48 .

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Factoring Part 3

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  1. FactoringPart 3 Wednesday, April 2nd

  2. Homework check!

  3. Factoring Warm-Up In your teams, factor the following: 16x4 – 20x3

  4. Factoring Warm-Up In your teams, factor the following: x2 – 12x + 20

  5. Factoring Warm-Up In your teams, factor the following: 2x2 – 10x – 48

  6. Factoring Warm-Up In your teams, factor the following: –4x2 – 8x – 4

  7. Factoring Quadratics:Review Decomposition Method Example: 3x2 – 5x – 2 Step #1: Write out your equation in form Ax2 + Bx + C Step #2: Multiply AC. Now look for a number that multiplies to AC and adds to B. Multiplies to -6 Adds to -5 Numbers are -6 and 1

  8. Factoring Quadratics:Review Decomposition Method 3x2– 6x + 1x– 2 Example: 3x2 – 5x – 2 Multiplies to -6 Adds to -5 Numbers are -6 and 1 Step #3: Re-write the middle term as the addition of the two numbers you found. 3x2 – 5x – 2

  9. Factoring Quadratics:Review Decomposition Method 3x2– 6x + 1x– 2 Example: 3x2 – 5x – 2 Multiplies to -6 Adds to -5 Numbers are -6 and 1 Step #4: Factor the first two terms of the polynomial and the last two terms seperately 3x(x – 2) + 1(x – 2)

  10. Factoring Quadratics:Review Decomposition Method 3x2– 6x + 1x– 2 Example: 3x2 – 5x – 2 Multiplies to -6 Adds to -5 Numbers are -6 and 1 3x(x – 2) + 1(x – 2) Step #5: Factor the common binomial out. 3x(x – 2) + 1(x – 2) (x – 2)(3x + 1)

  11. Factoring Quadratics:Triple Play Method Example: 5x2 – 11x + 2 Step #1: Write out your equation in form Ax2 + Bx + C Step #2: Multiply AC. Now look for a number that multiplies to AC and adds to B. Multiplies to 10 Adds to -11 Numbers are -10 and -1

  12. Factoring Quadratics:Triple Play Method Example: 5x2 – 11x + 2 Multiplies to 10 Adds to -11 Numbers are -10 and -1 Step #3: Write your equation in the form: (Ax )(Ax ) A (5x )(5x ) 5

  13. Factoring Quadratics:Triple Play Method Example: 5x2 – 11x + 2 Multiplies to 10 Adds to -11 Numbers are -10 and -1 Step #3: Write your equation in the form: (5x )(5x ) 5 Step #4: Fill in the blanks with the numbers you found (5x – 10)(5x – 1) 5

  14. Factoring Quadratics:Triple Play Method Example: 5x2 – 11x + 2 Multiplies to 10 Adds to -11 Numbers are -10 and -1 (5x – 10)(5x – 1) 5 Step #5: Divide only one of the brackets by the denominator (5x – 10)(5x – 1) 5 (x – 2)(5x – 1)

  15. Try in your teams Factor: 3x2 + x – 4 using BOTH the triple play method and decomposition Choose your favourite of the two methods and factor: –6x2+ 5x + 6 Extra challenge Factor: –17x + 3 + 10x2

  16. Factoring Higher Polynomials: Substitution Method Example: x4 – 4x2 – 45 Step #1: Substitute in A = x2so that you can make your equation look like a quadratic (x2)2 – 4(x2) – 45 A2 – 4A– 45 Step #2: Now factor it like a regular quadratic. Look for numbers that: Multiply to -45 Add to -4 Numbers are -9 and +5

  17. Factoring Higher Polynomials: Substitution Method Example: x4 – 4x2 – 45 A2 – 4A– 45 Where A = x2 (A – 9)(A + 5) Step #3: Replace A with x2 again. (x2 – 9)(x2+ 5)

  18. Factoring with Two Variables Example: x2 + 3xy + 2y2

  19. Factoring with Two Variables Example: x2 + 3xy + 2y2 Strategy: Treat these exactly like regular quadratics (x )(x ) Multiply to 2y2 Add to 3y Numbers are y and 2y (x + y)(x + 2y)

  20. Try in your teams Factor: x2 + xy – 6y2 Factor: x4 – 2x2 – 15 Extra challenge Factor: 4x4 – 5x2 – 6

  21. Summary Sheet & Khan Academy

  22. Homework: Page 163 #2 – 5 (ACEG)

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