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5.7 Synthetic Division

5.7 Synthetic Division. Algebra 2 Mrs. Spitz Fall 2006. Objective. Divide polynomials using synthetic division. Assignment. pg. 244 #4-29 all. Intro.

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5.7 Synthetic Division

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  1. 5.7 Synthetic Division Algebra 2 Mrs. Spitz Fall 2006

  2. Objective • Divide polynomials using synthetic division. Assignment • pg. 244 #4-29 all

  3. Intro • In lesson 5.6, you learned to divide a polynomial by another polynomial using long division. A simpler process is called synthetic division has been devised to divide a polynomial by a binomial. Study the examples to see how the process works.

  4. Ex. 1: Divide 2x3 – 7x2 – 8x + 16 by x - 4 4 2 -7 -8 16 8 4 -16 2 1 -4 0 The result is 2x2 + x – 4

  5. Let’s compare the process of synthetic division to long division. We have used both methods to divide 3x3 – 8x2 + 5x -1 by x – 2. 3x2 -2x +1 3x3 – 8x2 + 5x -1 2 3 -8 5 -1 6 -4 2 3x3 – 6x2 - + 3 -2 1 1 – 2x2 +5x -2x2 + 4x + - Compare the numbers in the second row of the synthetic division with those that appear in the long division. Why do you think that in synthetic division you add these numbers that you would subtract when using long division? Look at the divisors. x – 1 x – 2 - + 1

  6. Ex. 2: Use synthetic division to find (5s3 + s2 – 7)  (s + 1) • In synthetic division, every power of the variable must be represented by in the dividend, so 5s3 + s2 – 7 must be written as 5s3 + s2 +0s – 7 -1 5 1 0 – 7 The result is 5s2 – 4s + 4 -5 4 -4 5 -4 4 -11

  7. Check your work • To check the result, simply multiply the divisor, s + 1, by the quotient, 5s2 – 4s + 4. Then add the remainder, -11. It checks because the polynomial is the dividend.

  8. Ex. 3: Use synthetic division to find (x3 + 13x2 – 12x – 8)  (x + 2) -2 1 13 -12 -8 -2 -22 68 1 11 -34 60 The result is x2 +11x – 34 +

  9. Ex. 4: Use synthetic division to find (3y3 + 2y2 – 32y + 2)  (y – 3) 3 3 2 -32 2 9 33 3 3 11 1 5 The result is 3y2 +11y +1 +

  10. Ex. 5: Use synthetic division to find (2b3 + b2 – 2b + 3)  (b + 1) -1 2 1 -2 3 -2 1 1 2 -1 -1 4 The result is 2b2 – b – 1 +

  11. Ex. 6: Use synthetic division to find (y5 – 3y2 – 20)  (y – 2) 2 1 0 0 -3 -20 2 4 8 10 1 2 4 5 -10 The result is y4 + 2y3 + 4y2 +5y – 1 -

  12. Ex. 7: Use synthetic division to find (x3 + 3x2 – 7x + 1)  (x – 1) 1 1 3 -7 1 1 4 -3 1 4 -3 -2 The result is y2 – 4y – 3 –

  13. Upcoming • Monday – 5.6 • Wednesday 5.7 • Thursday – Chapter 5 Review • Friday – 6.1 • Monday – Review for semester final • Wednesday – Review for Semester Final • Thursday – Semester Final

  14. Upcoming • Friday – 6.2 • Monday – 6.3 • Wednesday 6.4 (Make up exams must be in by this date.) • Thursday – 6.5 • Friday – 6.6

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