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# 3/1/12 Factor by Grouping and Factoring into Quadratic Form

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### 3/1/12 Factor by Grouping and Factoring into Quadratic Form

1. 1. Bell Ringer <ul><li>Factor the following: </li></ul><ul><li>81x 3 – 192 </li></ul><ul><ul><ul><ul><li>3(3x - 4)(9x 2 + 4x + 16) </li></ul></ul></ul></ul><ul><ul><ul><ul><li>(3x- 4)(9x 2 + 4x + 16) </li></ul></ul></ul></ul><ul><ul><ul><ul><li>3(3x - 4)(9x 2 + 12x + 16) </li></ul></ul></ul></ul><ul><ul><ul><ul><li>(9x - 4)(9x 2 + 4x + 16) </li></ul></ul></ul></ul>Students will be able to factor polynomial equations. Page 356 #18-29, 32-40 (even)
2. 2. Today’s Lesson <ul><ul><li>Goal : Factor by Grouping & Factor Polynomials into Quadratic Form </li></ul></ul><ul><li>Factor by Grouping - factors out common terms, and then groups them. </li></ul><ul><li>For polynomials raised to higher powers, such as to the fourth power, we can factor into two quadratics. </li></ul>
3. 3. Factor by Grouping <ul><li>Pattern: </li></ul><ul><li>ra + rb +sa +sb = r ( a + b ) + s ( a + b ) </li></ul><ul><li>=( r + s )( a + b ) </li></ul>
4. 4. Factor by Grouping <ul><li>Example 1: </li></ul><ul><li>x 3 – 3x 2 –16x + 48 </li></ul><ul><li> x 2 ( x-3 ) – 16 ( x – 3 ) </li></ul><ul><li>( x 2 – 16 )( x-3 ) </li></ul>
5. 5. Factor by Grouping Exercises <ul><li>x 3 + 2x 2 + 3x + 6 m 3 – 2m 2 + 4m – 8 </li></ul>
6. 6. Factor into Quadratic Form <ul><li>Recall a quadratic is of the form: </li></ul><ul><li>ax 2 + bx 2 + c </li></ul><ul><li>Sometimes with higher powers, we factor our polynomial into quadratic form. </li></ul><ul><li>Example : x 4 – 81 </li></ul><ul><li>Think of rewriting x 4 as ( x 2 ) 2 </li></ul><ul><li>= ( x 2 + 9)( x 2 – 9) </li></ul><ul><li>= ( x 2 + 9)( x + 3)( x – 3) </li></ul>
7. 7. Factor into Quadratic Form <ul><li>16x 4 – 81 6y 6 – 5y 3 – 4 </li></ul>
8. 8. Factor into Quadratic Form <ul><li>Example 2 : </li></ul><ul><li>2x 8 + 10x 5 + 12x 2 </li></ul><ul><li>Factor common monomial </li></ul><ul><li>= 2x 2 (x 6 + 5x 3 + 6) </li></ul><ul><li>Factor our trinomial </li></ul><ul><li>= 2x 2 (x 3 + 3)(x 3 + 2) </li></ul>
9. 9. Challenge Problem <ul><li>The dimensions of a jewelry box are: length 4x, width (x-1), and height (x-2). If the volume of the box is 24 cubic inches, find the dimensions of the box. </li></ul><ul><li>Hint: Remember V=lwh . Multiply this out, and then try factoring by grouping to solve. </li></ul><ul><li>State the new dimensions, and show all of your work. </li></ul>
10. 10. Challenge Problem <ul><li>volume 24 in 3 , length 4x, width (x-1), height (x-2) </li></ul>
11. 11. Minute Paper <ul><li>1) What was the most important topic you learned today? </li></ul><ul><li>2) What did you like/dislike about the lesson? </li></ul><ul><li>3) How could I improve it? </li></ul>
12. 12. Homework <ul><li>Page 356 </li></ul><ul><li>#18-29; 32-40 (even) </li></ul><ul><li>Factor by Grouping </li></ul><ul><li>Factoring into Quadratics </li></ul><ul><li>Solve by Factoring </li></ul>