Mini-Lecture 6.4: Factoring Trinomials of the Form ax2+bx+c by Grouping | Lecture Note - Edubirdie

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

2023
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308

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1
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Oerallerxhcq

Mini-Lecture 6.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping Learning Objectives 1. Use the grouping method to factor trinomials of the form ax2 + bx + c. Examples: 1. Factor the following trinomial by grouping. Complete the outlined steps. a) 12y2 + 17y + 6 Find two numbers whose product is 72 (12 i 6) and whose sum is 17: ______ Write 17y using the factors from previous step: ______ Factor by grouping: ________ b) 10x2 + 9x - 9 Find two numbers whose product is −90 [10 i (−9) ] and whose sum is (-9): ______ Write (-9x) using the factors from part (a): ______ Factor by grouping: ________ Factor by grouping. c) 8x2 + 18x + 9 d) 6x2 + 7x - 3 e) 7x2 – 19x – 6 f) 4x2 - 12x + 9 g) 6x2 – 17x + 5 h) 20x2 - 15x – 50 i) 45x3 + 45x2 – 50x j) x – 15 + 6x2 k) 10z2 – 12z – 1 Teaching Notes: • • • • • Most students appreciate seeing the grouping method. This method gives the student a step-bystep guide to factoring. Encourage students to use whatever method works for them (trial-and-error or grouping). Remind students to put the trinomial into standard form before attempting to factor. Encourage students to check their factoring answers by multiplication. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 9,8; 9y+8y; (4y+3)(3y+2); 1b) -6, 15; -6x+15x; (5x-3)(2x+3); 1c) (4x+3)(2x+3); 1d) (2x+3)(3x-1); 1e) (7x+2)(x-3); 1f0 (2x-3)2; 1g) (2x-5)(3x-1); 1h) 5(x-2)(4x+5); 1i) 5x(3x-2)(3x+5); 1j) (3x+5)(2x-3); 1k) prime

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