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3.5 DIVIDING POLYNOMIALS
Using Long Division to Divide Polynomials Division of polynomials that contain more than one term has similarities to long division of whole numbers. We can write a polynomial dividend as the product of the divisor and the quotient added to the remainder. The terms of the polynomial division correspond to the digits (and place values) of the whole number division. This method allows us to divide two polynomials. EX. Divide 2x^3 − 3x^2 + 4x + 5 by x + 2 using the long division algorithm.
Using Synthetic Division to Divide Polynomials Synthetic division is a shortcut that can be used when the divisor is a binomial in the form x − k. In synthetic division, only the coefficients are used in the division process. EX. Divide 2x 3 − 3x 2
- 4x + 5 by x + 2 using the long division algorithm and then by Synthetic Division.
Try It # Divide 16x^3 − 12x^2 + 20x − 3 by 4x + 5.
EX. Use synthetic division to divide −9x 4
EX. The volume of a rectangular solid is given by the polynomial 3x^4 − 3x^3 − 33x^2 + 54x. The length of the solid is given by 3x and the width is given by x − 2. Find the height of the solid.
Try It # The area of a rectangle is given by 3x^3 + 14x^2 − 23x + 6. The width of the rectangle is given by x + 6. Find an expression for the length of the rectangle.
