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6.5 The Remainder and Factor Theorems
Goals p Divide polynomials and relate the result to the remainder theorem and the factor theorem. p Use polynomial division in real-life problems.
Your Notes VOCABULARY
Polynomial long division A method used to divide polynomials similar to the way you divide numbers
Synthetic division A method used to divide a polynomial by an expression of the form x k
Example 1 Using Polynomial Long Division
.Divide 4x4 ؊ x2 ؊ 18x ؉ 8 by x2 ؉ 2x ؉ 3 Write division in the same format you would use when dividing numbers. Include a “0” as the coefficient of x3. 4 3 2 4x 8x 3x x2 x2 x2
4x2 8x 3 x2 2x 3ͤ4ෆxෆ4ෆ ෆ0xෆ3ෆ ෆ1ෆ2ෆxෆ2ෆ ෆෆ18ෆxෆ ෆෆ8 4x4 8x3 12x2