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Ms. Cassidy’s Class

Ms. Cassidy’s Class. Welcome back, students!. 6.4 Factoring and Solving Polynomial Expressions. p. 345. Types of Factoring:. From Chapter 5 we did factoring of: GCF : 6x 2 + 15x = 3x (2x + 5) PTS : x 2 + 10x + 25 = (x + 5) 2 DOS : 4x 2 – 9 = (2x + 3)(2x – 3)

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Ms. Cassidy’s Class

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  1. Ms. Cassidy’s Class Welcome back, students!

  2. 6.4 Factoring and Solving Polynomial Expressions p. 345

  3. Types of Factoring: • From Chapter 5 we did factoring of: • GCF : 6x2 + 15x = 3x (2x + 5) • PTS : x2 + 10x + 25 = (x + 5)2 • DOS : 4x2 – 9 = (2x + 3)(2x – 3) • The Cassidy Way = 2x2 – 5x – 12 =

  4. Now we will use Sum of Cubes: • a3 + b3 = (a + b)(a2 – ab + b2) • THINK CUBE ROOT, CUBE ROOT AND SOAP: SQ 1ST, MULT. BOTH, SQ LAST • x3 + 8 = • (x)3 + (2)3 = • (x + 2)(x2 – 2x + 4)

  5. Difference of Cubes • a3 – b3 = (a – b)(a2 + ab + b2) • 8x3 – 1 = • (2x)3 – 13 = • (2x – 1)((2x)2 + 2x*1 + 12) • (2x – 1)(4x2 + 2x + 1)

  6. When there are more than 3 terms – use GROUPING • x3 – 2x2 – 9x + 18 = • Group in two’s • x2(x – 2) - 9(x – 2) = GCF each group • (x – 2)(x2 – 9) = • (x – 2)(x + 3)(x – 3) Factor all that can be • factored

  7. Factoring in Quad form (Try to look for diff. of 2 squares): • 81x4 – 16 = • (9x2 + 4)(9x2 – 4)= Can anything be • factored still??? • (9x2 + 4)(3x – 2)(3x +2) • Keep factoring ‘till you can’t factor any more!!

  8. You try this one! • 4x6 – 20x4 + 24x2 = • 4x2 (x4 - 5x2 +6) = • 4x2 (x2 – 2)(x2 – 3)

  9. In Chapter 5, we used the zero property. (when multiplying 2 numbers together to get 0 – one must be zero)The also works with higher degree polynomials

  10. Solve: • 2x5 + 24x = 14x3 • 2x5 - 14x3 + 24x = 0 Put in standard form • 2x (x4 – 7x2 +12) = 0 GCF • 2x (x2 – 3)(x2 – 4) = 0 Bustin’ da ‘b’ • 2x (x2 – 3)(x + 2)(x – 2) = 0 Factor • everything • 2x=0 x2-3=0 x+2=0 x-2=0 set all • factors to 0 • X=0 x=±√3 x=-2 x=2

  11. Now, you try one! • 2y5 – 18y = 0 • y=0 y=±√3 y=±i√3

  12. Assignment 348-349/18-84 mult of 3

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