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Factoring Polynomials Practice and Homework

Complete your homework by identifying multiples of 4, factor polynomials, and review factoring methods. Improve your understanding of factorization with various examples and exercises. Stay organized and focused for effective learning.

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Factoring Polynomials Practice and Homework

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  1. Do Now 3/15/10 • Take out your HW from Friday. • Text p. 603, #4-40 multiples of 4 • Copy HW in your planner. • Text p. 610, #4 – 40 multiples of 4 • In your notebook, list your thought process (questions you ask yourself) when you are given an expression to factor.(**Hint: think of the sections we have covered so far in Chapter 9)

  2. 4) (n + 8)(n – 8) 8) 9(5x + 4y)(5x – 4y) 12) (3t – 2)² 16) (2f – 9)² 20) 5(3r – 4s)² 24) A 28) +4/3, -4/3 32) +6, -6 36) +1/6, -1/6 40) +12, -12 HomeworkText p. 603, #4-40 multiples of 4

  3. Objective • SWBAT factor polynomials completely

  4. Factoring Polynomials Review • (9.5) Factor x² + bx + c • (9.6) Factor ax² + bx + c • (9.7) Factor special products x² – 7x – 30 (x – 10)(x + 3) 3z² + z – 14 (3z + 7)(z – 2) Perfect square trinomial Difference of two squares 72z² – 98 9z² – 36z + 36 (3z – 6)² 2(6z – 7)(6z + 7)

  5. Section 9.8 “Factor Polynomials Completely” • Factor out a common binomial- • 2x(x + 4) – 3(x + 4) • Factor by grouping- • x³ + 3x² + 5x + 15

  6. Factor out a common binomial 2x(x + 4) – 3(x + 4) Factor out the common binomial = (x + 4) (2x – 3) 2x(x + 4) – 3(x + 4) 4x²(x – 3) + 5(x – 3) Factor out the common binomial = (x – 3) 4x²(x – 3) + 5(x – 3) (4x² + 5)

  7. Factor out a common binomial 7y(y – 2) + 3(2 – y) The binomials y – 2 and 2 – y are opposites. Factor out -1 from 3(2 – y) to obtain -3(y – 2). 7y(y – 2) – 3(y – 2) Factor out the common binomial = (y – 2) 7y(y – 2) – 3(y – 2) (7y – 3)

  8. Factor out a common binomial…Try It Out 2y²(y – 4) – 6(4 – y) The binomials y – 4 and 4 – y are opposites. Factor out -1 from -6(4 – y) to obtain 6(y – 4). 2y²(y – 4) + 6(y – 4) Factor out the common binomial = (y – 4) 2y²(y – 4) + 6(y – 4) (2y² + 6)

  9. Factor by grouping x³ + 3x² + 5x + 15 Group terms into binomials and look to factor out a common binomial. (x³ + 3x²) + (5x + 15) x² (x + 3) + 5 (x + 3) Factor out each group Factor out the common binomial = (x + 3) x²(x + 3) + 5(x + 3) (x² + 5)

  10. Factor by grouping…Try It Out Reorder polynomial with degree of powers decreasing from left to right. x³ – 6 + 2x – 3x² x³ – 3x² + 2x – 6 Group terms into binomials and look to factor out a common binomial. (x³ – 3x²) + (2x – 6) x² (x – 3) + 2 (x – 3) Factor out each group Factor out the common binomial = (x – 3) x²(x – 3) + 2(x – 3) (x² + 2)

  11. Factoring Polynomials Completely • (1) Factor out greatest common monomial factor. • (2) Look for difference of two squares or perfect square trinomial. • (3) Factor a trinomial of the form ax² + bx + c into binomial factors. • (4) Factor a polynomial with four terms by grouping. 3x² + 6x = 3x(x + 2) x² + 4x + 4 = (x + 2)(x + 2) 16x² – 49 = (4x + 7)(4x – 7) 3x² – 5x – 2 = (3x + 1)(x – 2) -4x² + x + x³ - 4 = (x² + 1)(x – 4)

  12. Homework • Text p. 610, #4 – 40 multiples of 4

  13. SET 1 a) (a + 4)(a + 5) b) (a – 4)(a + 6) c) (a + 8)(a – 8) d) (a – 1)(5a + 4) e) (5a + 2)(5a + 2) HomeworkPunchline worksheet 13.11 “Why Did the Boy Sheep Plunge Off a Cliff While Chasing the Girl Sheep?” SET 3 • a) (k + 3)(8k + 1) • b) (2k + 3)(4k – 1) • c) (k – 1)(4k – 11) • d) (2k + 11)(2k – 11) • e) (k – 2)(11k + 8) SET 2 • a) (u – 3)(2u – 5) • b) (7 + 4u)(7 – 4u) • c) (u – 7)(2u + 5) • d) (u – 2)(7u + 2) • e) (7u – 4)(7u – 4) SET 4 • a) (9x² + y)(9x² – y) • b) (x – 5y)(3x – 8y) • c) (9x + y)(9x + y) • d) (3x – y)(3x + 8y) • e) (x + 4y)(9x + 2y) “HE DIDN’T SEE THE EWE TURN”

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