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8.4 Dividing Polynomials

8.4 Dividing Polynomials. CORD Math Mrs. Spitz Fall 2006. Objective. Divide polynomials by binomials. Upcoming. 8.4 Monday 10/23 8.5 Tuesday/Wednesday – Skip 8.6 8.7 Thursday 10/26 8.8 Friday 10/27 8.9 Monday 10/30 8.10 Tuesday/Wed Chapter 8 Review Wed/Thur Chapter 8 Test Friday.

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8.4 Dividing Polynomials

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  1. 8.4 Dividing Polynomials CORD Math Mrs. Spitz Fall 2006

  2. Objective • Divide polynomials by binomials

  3. Upcoming • 8.4 Monday 10/23 • 8.5 Tuesday/Wednesday – Skip 8.6 • 8.7 Thursday 10/26 • 8.8 Friday 10/27 • 8.9 Monday 10/30 • 8.10 Tuesday/Wed • Chapter 8 Review Wed/Thur • Chapter 8 Test Friday

  4. Assignment • Pg. 320 #3-31 all

  5. Introduction • To divide a polynomial by a polynomial, you can use a long division process similar to that used in arithmetic. For example, you can divide x2 + 8x +15 by x + 5 as shown on the next couple of slides.

  6. Step 1 • To find the first term of the quotient, divide the first term of the dividend (x2) by the first term of the divisor (x). x 3x + 15

  7. Step 2 • To find the next term of the quotient, divide the first term of the partial dividend (3x) by the first term of the divisor (x). x + 3 3x + 15 3x - 15 0 Therefore, x2 + 8x + 15 divided by x + 5 is x + 3. Since the remainder is 0, the divisor is a factor of the divident. This means that (x + 5)(x + 3) = x2 + 8x + 15.

  8. What happens if it doesn’t go evenly? • If the divisor is NOT a factor of the dividend, there will be a non-zero remainder. The quotient can be expressed as follows: Quotient = partial quotient +

  9. Ex. 1: Find (2x2 -11x – 20)  (2x + 3). x - 7 ← Multiply by x(2x+3) - 14x - 20 ← Subtract, then bring down - 20 + 14x+ 21 ← Multiply -7(2x+3) + 1 ← Subtract. The remainder is 1 The quotient is x – 7 with a remainder of 1. Thus, (2x2 -11x – 20)  (2x + 3) = x – 7 +

  10. Other note . . . • In an expression like s3 +9, there is no s2 term and no s term. In such situations, rename the expression using 0 as a coefficient of these terms as follows: s3 + 9 = s3 + 0s2 + 0s + 9

  11. Ex. 2: Find s2+3s + 9 ← Insert 0s2 and 0s. Why? ← Multiply by s2 3s2 + 0s ← Subtract, then bring down 0s 3s2 - 9s ← Multiply 3s(s - 3) 9s + 9 -9s + 27 ← Subtract. The remainder is 36 + 36 The quotient is s2+3s+9 with a remainder of 36. Thus, (s3 + 9)  (s - 3) = s2 + 3s + 9 +

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