9 6 Factoring Special Polynomials

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9 6 Factoring Special Polynomials

  1. 1. Factoring Special Polynomials Holt Text pages 452-454
  2. 2. Perfect Square Polynomials <ul><li>Examples </li></ul><ul><ul><li>(x+2) 2 </li></ul></ul><ul><ul><li>(x-3) 2 </li></ul></ul>
  3. 3. Terminology <ul><li>Perfect Square Polynomials </li></ul><ul><ul><li>First term is a perfect square </li></ul></ul><ul><ul><li>Last term is also a perfect square </li></ul></ul><ul><ul><li>Middle Term: Multiply the square root of the first and last terms, then double it. </li></ul></ul><ul><ul><li>Is x 2 + 12x + 36 a perfect square polynomial? </li></ul></ul>
  4. 4. x 2 +8 x+16 <ul><li>What is the square root of: </li></ul><ul><ul><li>x 2 ? </li></ul></ul><ul><li>16? </li></ul><ul><li>What is 2(x)(4)? </li></ul><ul><li>Is x 2 +8 x+16 a perfect square. </li></ul>
  5. 5. 3x 2 +3 x+16 <ul><li>What is the square root of: </li></ul><ul><ul><li>3x 2 ? </li></ul></ul><ul><li>16? </li></ul><ul><li>Is 3 x 2 +16 x+16 a perfect square? </li></ul>
  6. 6. x 2 +3 x+9 <ul><li>What is the square root of: </li></ul><ul><ul><li>x 2 ? </li></ul></ul><ul><li>16? </li></ul><ul><li>What is 2(x)(4)? </li></ul><ul><li>Is x 2 +8 x+16 a perfect square? </li></ul>
  7. 7. Factor 9x 2 +24 x+16 <ul><li>Since the sq. root of 9x 2 is 3x </li></ul><ul><li>Since the sq. root of 16 is 4 </li></ul><ul><li>(3x+4) 2 equals the above polynomial. </li></ul>
  8. 8. Factor 64x 4 -16 x 2 y+y 2 <ul><li>Since the sq. root of 64x 4 is 3x </li></ul><ul><li>Since the sq. root of y 2 is 4 </li></ul><ul><li>(8x 2 +y) 2 equals the above polynomial. </li></ul>
  9. 9. Difference of Two Squares <ul><li>Factor 4x 2 -25 </li></ul><ul><li>Negative constants have a negative and positive factor </li></ul><ul><li>Positive square numbers have two positive factors </li></ul>
  10. 10. Factor 4x 2 -25 <ul><li>The square root of the first term: 4x </li></ul><ul><li>The positive and negative factors of -25 are -5 and +5 </li></ul><ul><li>This converts to (2x-5)(2x+5) </li></ul><ul><li>Notice the only difference between the difference of two squares and (2x+5)(2x+5). </li></ul>
  11. 11. Factor 16x 2 -49 <ul><li>The square root of the first term: 4x </li></ul><ul><li>The positive and negative factors of -49 are -7 and +7 </li></ul><ul><li>This converts to (4x-7)(4x+7) </li></ul>
  12. 12. Factor x 2 -4 <ul><li>The square root of the first term: x </li></ul><ul><li>The positive and negative factors of -49 are -2 and +2 </li></ul><ul><li>This converts to (x-2)(x+2) </li></ul>
  13. 13. Factor 81x 2 -64 <ul><li>The square root of the first term: 9x </li></ul><ul><li>The positive and negative factors of -64 are -8 and +8 </li></ul><ul><li>This converts to (9x-8)(9x+8) </li></ul>

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