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Dividing Polynomials; Remainder and Factor Theorems

Dividing Polynomials; Remainder and Factor Theorems In this section we will learn how to divide polynomials, an important tool needed in factoring them. This will begin our algebraic study of polynomials. Dividing by a Monomial: Recall from the previous section that a monomial is a single term, such as 6x3 or 7. To divide a polynomial by a monomial, divide each term in the polynomial by the monomial, and then write each quotient in lowest terms. Example 1: Divide 9x4 + 3x2 5x + 6 by 3x. Solution: Step 1: Divide each term in the polynomial 9x4 + 3x2 5x + 6 by the monomial 3x.

monomial 3x. 93 569 3 5 642 4 2 3333 xxx x x x. x xx x3 +−+ =+ −+ x. Step 2: Write the result in lowest terms. 42 93 5 6 53 3 33 33 3 xxx xx. 2 x xx x +−+=+−+ x. Thus, 9x4 + 3x2 – 5x + 6 divided by 3x is equal to . 3 52 3 3 xx. x + −+ Long Division of Polynomials: To divide a polynomial by a polynomial that is not a monomial we must ...

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