Mini-Lecture 5.6: Dividing Polynomials | Montgomery College - Edubirdie

University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
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346

Pages:

1
Author:

Ean Mason

Mini-Lecture 5.6 Dividing Polynomials Learning Objectives: 1. Divide a polynomial by a monomial. 2. Use long division to divide a polynomial by another polynomial. Examples: 1. Perform each division. a) 10 x 6 − 40 x3 b) 5x2 6a 7 − 10a5 c) −2a 7 −14 x 7 + 6 x6 − 6 x5 −2 x5 2. Find each quotient using long division. a) x 2 + 9 x + 20 x+5 b) 6m3 + 26m 2 − 17 m + 15 m+5 c) −20 x3 + 17 x 2 + 15 x + 13 −5 x − 2 d) ( 4m 3 ) + 14m 2 − 5m + 12 ÷ ( m + 4 ) Find each quotient using long division. Don’t forget to write the polynomials in descending order and fill in any missing terms. e) (x 4 ) + 81 ÷ ( x − 3) f) 9 − 5 x − 25 x3 − 15 x 2 −5 x + 2 Teaching Notes: • • • • Encourage students to write out each step before simplifying in 1a), 1b), 1c). Many students will “cancel” the monomial and one of the terms instead of dividing. Most students will need slow, methodical modeling to understand the concept of dividing by a monomial. Many students need to see a numerical long division done in parallel with long division of polynomials. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 2x4-8x; 1b) − 3 + 5 11 ; 1c) 7x2-3x+3; 2a) x+4; 2b) 6m2-4m+3; 2c) 4x2-5x-1+ ; 2 −5 x − 2 a 2d) 4m2-2m+3; 2e) x3+3x2+9x+27+ 162 3 ; 2f) 5x2+5x+3+ −5 x + 2 x−3

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