Section 3-1.3 - ) ( ) ( ) ( ) ( x r x q x d x f !...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
3.3 – Dividing Polynomials; Remainder and Factor Theorems The polynomials that we solved thus far have been factorable using basic factoring rules. In order to work with polynomials that do not factor as easily, we need to first review division of polynomials. Long Division of Polynomials 1. Arrange the terms in the dividend and the divisor in descending powers of the variable. Use zero placeholders for any missing terms. 2. Divide the first term in the dividend by the first term in the divisor. This result becomes the first term in the quotient. 3. Multiply this new term by each term in the divisor and create a new row. 4. Subtract rows. 5. Bring down the remaining terms in the dividend and repeat from Step 2. 6. The process will stop once the degree of the remaining polynomial on the inside is less than the degree of the divisor. You can write your final answer in one of two ways: the quotient plus the remainder as a fraction of the divisor OR use the division algorithm. Division Algorithm
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) ( ) ( ) ( ) ( x r x q x d x f ! " # f = dividend d = divisor q = quotient r = remainder ! Example 1 Divide 7 11 3 2 2 3 ! $ $ x x x by 3 $ x . " ! Example 2 Divide 10 7 3 2 2 3 $ $ ! x x x by x x 2 2 $ . " If the divisor is of the form c x $ where c is a constant (positive or negative), then the long division process can be replaced by synthetic division . In synthetic division, only the coefficients are used. The quotient will always be one degree less than the dividend. ! Example 3 Use synthetic division to divide 6 7 3 $ $ x x by 2 ! x . " Remainder Theorem If the polynomial ) ( x f is divided by c x $ , then the remainder is equal to ) ( c f . ! Example 4 Given 3 5 4 3 ) ( 2 3 ! $ ! # x x x x f , use the Remainder Theorem to find ) 4 ( $ f . " Factor Theorem If ) ( # c f , then c x $ is a factor of ) ( x f . If c x $ is a factor of ) ( x f , then ) ( # c f . ! Example 5 Solve the equation 2 3 14 15 2 3 # $ $ ! x x x given that -1 is a zero of the function. "...
View Full Document

Page1 / 3

Section 3-1.3 - ) ( ) ( ) ( ) ( x r x q x d x f !...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online