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6-3: Dividing Polynomials

6-3: Dividing Polynomials. Essential Question: What does the last number in the bottom line of synthetic division represent?. 6-3: Dividing Polynomials. Using Long Division Polynomial Long division works similarly to regular long division (I know… it’s been a while) Divide 1,732,042 by 440.

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6-3: Dividing Polynomials

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  1. 6-3: Dividing Polynomials Essential Question: What does the last number in the bottom line of synthetic division represent?

  2. 6-3: Dividing Polynomials • Using Long Division • Polynomial Long division works similarly to regular long division (I know… it’s been a while) • Divide 1,732,042 by 440 Answer is 3936, R: 202

  3. 6-3: Dividing Polynomials • Divide x2 + 3x – 12 by x – 3 Answer is x + 6, R: 6

  4. 6-3: Dividing Polynomials • Your Turn • Divide x2 – 3x + 1 by x – 4 Answer is x + 1, R: 5

  5. 6-3: Dividing Polynomials • We can use division to find factors of a polynomial. • If the remainder of division comes out to be 0, then the divisor (and quotient) are factors. • Determine whether x + 4 is a factor of the polynomial x2 + 6x + 8. Because the remainder is 0, x + 4 IS a factor of x2 + 6x + 8 (so is x + 2)

  6. 6-3: Dividing Polynomials • Determine whether x + 4 is a factor of the polynomial x3 + 3x2 – 6x – 7. Because the remainder is not 0, x + 4 IS NOT a factor of x3 + 3x2 – 6x – 7

  7. 6-3: Dividing Polynomials • Your Turn • Determine whether x – 8 is a factor of the polynomial 2x2 – 19x + 24. Because the remainder is 0, x – 8 IS a factor of 2x2 – 19x + 24

  8. 6-3: Dividing Polynomials • Your Turn • Determine whether x + 2 is a factor of the polynomial x3 – 4x2 + 3x +2. Because the remainder is not 0, x + 2 IS NOT a factor of x3 – 4x2 + 3x + 2

  9. 6-3: Dividing Polynomials • Assignment • Page 324 • Problems 1 – 12 (all problems) • Obviously, show your work • Tomorrow • Quiz review • Next week • The secrets of synthetic division • Chapter 6 Test

  10. Unit #4: Polynomials6-3: Dividing PolynomialsDay 2 Essential Question: What does the last number in the bottom line of synthetic division represent?

  11. 6-3: Dividing Polynomials • Synthetic Division • Can only be used when the divisor is “x” +/- some constant (e.g. “x + 2”, “x – 10”) • Step 1: Reverse the sign of the constant terms in the divisor. Write the coefficients of the polynomial in standard form. • Step 2: Bring down the first coefficient • Step 3: Multiply the first coefficient by the new divisor. Write the result under the next coefficient. Add. • Step 4: Repeat the steps of multiplying and adding until the remainder is found. • Step 5: The quotient begins one degree less than the dividend.

  12. 6-3: Dividing Polynomials • Divide 3x3 – 4x2 + 2x – 1 by x + 1

  13. 6-3: Dividing Polynomials • Divide 3x3 – 4x2 + 2x – 1 by x + 1

  14. 6-3: Dividing Polynomials • Divide 3x3 – 4x2 + 2x – 1 by x + 1

  15. 6-3: Dividing Polynomials • Divide 3x3 – 4x2 + 2x – 1 by x + 1

  16. 6-3: Dividing Polynomials • Divide 3x3 – 4x2 + 2x – 1 by x + 1 • The quotient is 3x2 – 7x + 9, R: -10

  17. 6-3: Dividing Polynomials • Your Turn • Divide x3 – 4x2 + x – 6 by x – 3 Answer is x2 – 1x – 2, R: -12

  18. 6-3: Dividing Polynomials • Assignment • Page 324 – 325 • Problems 13 – 22 & 48 – 51 (all problems) • Obviously, show your work • Tomorrow • Chapter 6 Review Packet will be distributed

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