# 4.8b SKM & PP 1 Division of Polynomials. 4.8b SKM & PP 2 Division of Polynomials First, let’s review the symbols that represent the division problem:

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4.8b SKM & PP 1 Division of Polynomials

4.8b SKM & PP 2 Division of Polynomials First, let’s review the symbols that represent the division problem: “a divided by b”

4.8b SKM & PP 3 How to Write: “Seventeen divided by five”

4.8b SKM & PP 4 Division of Polynomials Now let’s review the terminology for the parts of a division problem. Divisor Quotient Remainder Dividend Division Symbol

4.8b SKM & PP 5 Long Division Review the Terminology Divisor Quotient Remainder Dividend Division Symbol Equal Symbol “Seventeen divided by five”

4.8b SKM & PP 6 Long Division Divisor Quotient Remainder Dividend Division Symbol Equal Symbol “Seventeen divided by five”

4.8b SKM & PP 7 Long Division Divisor Quotient Fractional Remainder Dividend Division Symbol “Seventeen divided by five”

4.8b SKM & PP 8 12417 Long Division Study the steps! 34 36 57 48 9 3 4 9 12

4.8b SKM & PP 9 Polynomial Long Division: Steps The same steps are used to divide a polynomial by a binomial: 1. Divide 2. Multiply 3. Subtract 4. Bring Down

4.8b SKM & PP 10 x-2x2x2 - 13x+ 22 Example 1: Divide Multiply Subtract Bring Down + 22 Divide Multiply Subtract

4.8b SKM & PP 11 x- 11 x-2x2x2 - 13x+ 22 x2x2 - 2x -11x+ 22 -11x+ 22 0 Example 1: To check our answer, multiply the divisor and the quotient: (x - 2)(x - 11) = x 2 - 13x + 22

4.8b SKM & PP 12 3x-212x 2 + 13x- 14 Example 2: Divide Multiply Subtract Bring Down -14 Divide Multiply Subtract

4.8b SKM & PP 13 4x+ 7 3x-212x 2 + 13x- 14 12x 2 - 8x 21x- 14 21x- 14 0 Example 2: To check our answer, multiply the divisor and the quotient: (3x - 2)(4x + 7) = 12x 2 + 13x -14

4.8b SKM & PP 14 Example 3: -3 3x- 42x+1 6x 2 - 5x- 7 6x 2 + 3x -8x- 7 -8x- 4 - 3

4.8b SKM & PP 15 Example 3: -3 3x- 42x+1 6x 2 - 5x- 7 6x 2 + 3x -8x- 7 -8x- 4 - 3 Check: divisor times quotient plus remainder (2x+1)(3x-4) + (-3) = 6x 2 - 8x + 3x - 4 – 3 = 6x 2 - 5x -7

4.8b SKM & PP 16 x 2 + x+ 1 x-1x3x3 + 0x 2 + 0x 1 - 1 x3x3 - x 2 x 2 + 0x x 2 - x x- 1 x 0 Example 4: Remember to put in place holders for the missing powers of x.

4.8b SKM & PP 17 That’s All for Now!

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