Digital Lesson Division of Polynomials Dividing Polynomials Long

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Digital Lesson Division of Polynomials

Digital Lesson Division of Polynomials

Dividing Polynomials Long division of polynomials is similar to long division of whole numbers.

Dividing Polynomials Long division of polynomials is similar to long division of whole numbers. When you divide two polynomials you can check the answer using the following: dividend = (quotient • divisor) + remainder The result is written in the form: quotient + Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2

Example: Divide x 2 + 3 x – 2 by x – 1 and

Example: Divide x 2 + 3 x – 2 by x – 1 and check the answer. x + 2 x 2 + x 2 x – 2 2 x + 2 – 4 remainder Answer: x + 2 + 1. 2. 3. 4. 5. 6. – 4 Check: (x + 2) (x + 1) + (– 4) = x 2 + 3 x – 2 correct quotient divisor remainder Copyright © by Houghton Mifflin Company, Inc. All rights reserved. dividend 3

Example: Divide 4 x + 2 x 3 – 1 by 2 x –

Example: Divide 4 x + 2 x 3 – 1 by 2 x – 2 and check the answer. x 2 + x + 3 2 x 3 – 2 x 2 + 4 x 2 x 2 – 2 x 6 x – 1 6 x – 6 5 Answer: x 2 +x+3 5 Write the terms of the dividend in descending order. Since there is no x 2 term in the dividend, add 0 x 2 as a placeholder. 1. 3. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 4. 5. 6. 7. Check: (x 2 + x + 3)(2 x – 2) + 5 = 4 x + 2 x 3 – 1 2. 8. 9. 4

Example: Divide x 2 – 5 x + 6 by x – 2. x

Example: Divide x 2 – 5 x + 6 by x – 2. x – 3 x 2 – 2 x – 3 x + 6 0 Answer: x – 3 with no remainder. Check: (x – 2)(x – 3) = x 2 – 5 x + 6 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 5

Example: Divide x 3 + 3 x 2 – 2 x + 2 by

Example: Divide x 3 + 3 x 2 – 2 x + 2 by x + 3 and check the answer. x 2 + 0 x – 2 Note: the first subtraction eliminated two terms from the dividend. Therefore, the quotient skips a term. Answer: x 2 – 2+ 8 x 3 + 3 x 2 0 x 2 – 2 x + 2 – 2 x – 6 8 Check: (x + 3)(x 2 – 2) + 8 = x 3 + 3 x 2 – 2 x + 2 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 6