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Welcome Back! Factoring and Solving Polynomial Expressions in Ms. Cassidy's Class

Welcome back, students of Ms. Cassidy’s class! In this lesson, we will review factoring techniques, including GCF, Perfect Squares, and the Difference and Sum of Cubes. We'll apply these methods to polynomial expressions, emphasizing grouping when necessary. Remember the zero property to solve higher degree polynomials. We’ll cover specific examples such as factoring (2x^5 + 24x = 14x^3) and give you practice problems to solidify your understanding. Get ready to dive into math and tackle the challenges ahead!

kessie-garrett
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Welcome Back! Factoring and Solving Polynomial Expressions in 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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