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Do Now 2/27/19

Enhance your polynomial factoring skills with guided exercises and examples. Learn to factor different types of expressions. Practice factoring polynomials completely. Use common binomials, special products, and grouping techniques for efficient factoring. Improve your problem-solving skills. Master the art of simplifying and solving polynomial equations.

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Do Now 2/27/19

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  1. Do Now 2/27/19 • Take out your HW from last night. • Punchline worksheet 13.11 • Copy HW in your planner. • Text p. 407, #4-36 evens • In your notebook, list your thought process (questions you ask yourself) when you are given an expression to factor. Then factor the 5 expressions to the right. 3x² + 6x x² + 4x + 4 16x² – 49 x² – 7x + 10 3x² – 5x – 2

  2. Factoring Polynomials Completely 3x² + 6x = 3x(x + 2) • (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 x² + bx + c into binomial factors. • (4) Factor a trinomial of the form ax² + bx + c into binomial factors. • (5) Factor a polynomial with four terms by grouping. x² + 4x + 4 = (x + 2)(x + 2) 16x² – 49 = (4x + 7)(4x – 7) x² – 7x + 10 = (x – 2)(x – 5) 3x² – 5x – 2 = (3x + 1)(x – 2) -4x² + x + x³ - 4

  3. 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”

  4. Learning Goal • SWBAT simplify, factor, and solve polynomial expressions and equations Learning Target • SWBAT factor polynomials completely

  5. Factoring Polynomials Review 6x² – 12x 6x(x – 2) • (7.4)Greatest Common Factor • (7.5) Factor x² + bx + c • (7.6) Factor ax² + bx + c • (7.7) 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 z² – 12z + 36 (z – 6)² 2(6z – 7)(6z + 7)

  6. Section 7.8 “Factor Polynomials Completely” • Factor out a common binomial- • 2x(x + 4) – 3(x + 4) • Factor by grouping- • x³ + 3x² + 5x + 15

  7. 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)

  8. 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)

  9. 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) = 2(y² + 3) (y – 4)

  10. 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)

  11. 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)

  12. Problem Solving Volume = length x width x height (16 – w) • A box has a volume of 768 cubic inches and all three sides are different lengths. The dimensions of the box are shown. Find the width, length, and height. (w) (w + 4) Substitute the possible solutions to see which dimensions work out. w = 12 w = 8 8 4 8 12 12 16 w = -8 w = 8 w = 12 Volume = 12 x 16 x 4 Can’t have negative width

  13. Factoring Polynomials Completely 4x² + 10x = 2x(2x + 5) • (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 x² + bx + c into binomial factors. • (4) Factor a trinomial of the form ax² + bx + c into binomial factors. • (5) Factor a polynomial with four terms by grouping. x² + 4x + 4 = (x + 2)(x + 2) 16x² – 49 = (4x + 7)(4x – 7) x² – 7x + 10 = (x – 2)(x – 5) 3x² – 5x – 2 = (3x + 1)(x – 2) -4x² + x + x³ - 4 = (x² + 1)(x – 4)

  14. Homework • Text p. 407, #4-36 evens

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