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- 1. Bell Ringer Factor the following: x 2 – 81 x 2 +10x +25 1. 2. Students will be able to factor polynomial equations. Page 356 #3-17
- 2. Today’s Lesson <ul><ul><li>Goal : Factor Sum & Differences of Cubes </li></ul></ul><ul><li>Factoring cubes is similar to factoring special cases with quadratics. </li></ul><ul><li>Questions to consider: </li></ul><ul><ul><li>What is a cube? </li></ul></ul><ul><ul><li>How do you think we might factor one? </li></ul></ul><ul><ul><li>What is the purpose of factoring? </li></ul></ul>
- 3. Cubes, Cubes, & More Cubes <ul><li>Let’s make a list of cubes! </li></ul>
- 4. Sum & Difference of Cubes <ul><li>Sum of Cubes: </li></ul><ul><li>a 3 + b 3 = ( a + b )( a 2 – ab + b 2 ) </li></ul><ul><li>Difference of Cubes: </li></ul><ul><li>a 3 – b 3 = ( a – b )( a 2 + ab + b 2 ) </li></ul>
- 5. Sum of two Cubes Example <ul><li>Factor the following: </li></ul><ul><li>x 3 + 27 </li></ul><ul><li>a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) </li></ul><ul><li>x 3 + 27 = (x) 3 + (3) 3 </li></ul><ul><li>= (x + 3)[(x) 2 − (x)(3) + (3) 2 ] </li></ul><ul><li>= (x + 3)(x 2 − 3x + 9) </li></ul>1, 8, 27, 64, 125, 216, 343, 512, 729, 1000…
- 6. Difference of two Cubes Example <ul><li>Factor the following: </li></ul><ul><li>x 3 - 64 </li></ul><ul><li> a 3 – b 3 = ( a – b )( a 2 + ab + b 2 ) </li></ul><ul><li>x 3 - 64 = (x) 3 - (4) 3 </li></ul><ul><li>= (x - 4)[(x) 2 + (x)(4) + (4) 2 ] </li></ul><ul><li>= (x - 4)(x 2 +4x + 16) </li></ul>1, 8, 27, 64, 125, 216, 343, 512, 729, 1000…
- 7. Exercises <ul><li>x 3 – 125 </li></ul><ul><li>x 3 + 216 </li></ul>
- 8. Exercises <ul><li>8x 3 – 1 </li></ul><ul><li>27x 3 +343 </li></ul>
- 9. Factor a Common Monomial <ul><li>Take out our greatest common factor! </li></ul><ul><li>Our goal is to “factor the polynomial completely.” </li></ul><ul><li>Example : </li></ul><ul><li>3x 4 +9x 2 – 6x </li></ul><ul><li>= 3x(x 3 +3x – 2) </li></ul>
- 10. Factoring a Common Monomial Exercises <ul><li>3x 3 + 9x 2 – 81 </li></ul><ul><li>4x 4 - 16x 3 + 16x 2 </li></ul><ul><li>2x 5 – 18x 3 </li></ul>
- 11. Homework <ul><li>Page 356 </li></ul><ul><li>#3-17 </li></ul><ul><li>Sum or Difference of Cubes </li></ul><ul><li>Monomial Factors </li></ul>

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