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

2023
Views:

465

Pages:

1
Author:

Zoie Hudson

Mini-Lecture 6.1 The Greatest Common Factor and Factoring by Grouping Learning Objectives: 1. Find the greatest common factor of a list of integers. 2. Find the greatest common factor of a list of terms. 3. Factor out the greatest common factor from a polynomial. 4. Factor a polynomial by grouping. Examples: 1. Find the greatest common factor for each list. a) 16, 6 b) 18, 24 c) 15, 21 d) 12, 28, 40 c) -28x4, 56x5 d) 21m2n5, 35mn4 2. Find the GCF for each list. a) 15m2, 25m5 b) 40x2 , 20x7 3. Factor out the GCF from each polynomial. a) 5a + 15 b) 56z + 8 c) y3 + 2y d) 5x3 + 10x4 e) 16z5 + 8z3 – 12z f) x(y2 – 2) + 3(y2 – 2) g) 6a8b9 – 8a3b4 + 2a2b3 + 4a5b3 4. Factor each four-term polynomial by grouping. a) 8y2 – 12y + 10y - 15 b) 15a6 – 25a3 – 6a3 + 10 c) 15x3 – 25x2y –6xy2 + 10y3 Teaching Notes: • • • • • Many students remove common factors, not the greatest common factor. Encourage students to factor in a step-by-step manner: first factor out the GCF for the coefficients, then the GCF for each variable. Most students have trouble factoring by grouping when it entails factoring a negative from the second group. Encourage students to always write a sign and check by distributing. If the check has the correct terms but wrong sign; switch the sign. Remind students that they can check their work by multiplying. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 2; 1b) 6; 1c) 3; 1d) 4; 2a) 5m2; 2b) 20x2; 2c) -28x4; 2d) 7mn4; 3a) 5(a+3); b) 8(7z+1); 3c) y(y2+2); 3d) 5x3(1+2x); 3e) 4z(4z4+2z2-3); 3f) (y2-2)(x+3); 3g)2a2b3(3a6b6-4ab+1+2a3); 4a)(2y-3)(4y+5); 4b) (3a3-5)(5a3-2); 4c) (3x-5y)(5x2-2y2)