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

2023
Views:

447

Pages:

1
Author:

Nyasia Cardenas

Mini-Lecture 6.3 Factoring Trinomials of the Form ax2 + bx + c and Perfect Square Trinomials Learning Objectives 1. Factor trinomials of the form ax2 + bx + c, where a ≠ 1. 2. Factor out the GCF before factoring a trinomial of the form ax2 + bx + c. 3. Factor perfect square trinomials. Examples; 1. Complete each factored form. a) 3x2 + 8x + 4 = (3x + 2)( ) b) 2y2 + 7y – 15 = (2y – 3)( ) Factor each trinomial completely. c) 2x2 + 7x + 3 d) 5x2 + 17x + 6 e) 8x2 + x – 7 f) 20r2 + 31r – 7 g) 6x2 + 19x – 11 h) 3x2 – 7x –20 2. Factor each trinomial completely. If necessary, factor out the GCF first. a) 14x2+ 4x – 10 b) 9x2 – 6x – 15 c) 14x3 + 66x2 – 20x d) 25x3 – 15x2 – 10x e) 4x2y2 – xy2 – 105y2 f) 12x2 – 25xt +12t2 g) -7x2 –33x + 10 h) 18x4 – 3x3 – 21x2 i) 2x5 – x3y2 – 15xy4 3. Factor each Perfect Square Trinomial completely. a) x 2 + 2 x + 1 b) 4 x 2 − 12 x + 9 c) 25 x 2 + 60 xy + 36 y 2 d) 16 x3 − 8 x 2 y + xy 2 e) 5 x3 − 10 x 2 + 5 x f) 2a − 24ay + 72ay 2 Teaching Notes: • Some students remember factoring from high school and are able to use the trial-and-error method to factor. • Some students may need to see Section 4.4, Factoring Trinomials by Grouping before being able to factor successfully. • Encourage students to use strategies when factoring. For example, identify any prime numbers to reduce the number of combinations. • Many students will forget to put the GCF in their final answer. • 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) (x+2); 1b) (y+5); 1c) (2x+1)(x+3); 1d) (5x+2)(x+3); 1e) (8x-7)(x+1); 1f) (5r-1)(4r+7); 1g) (3x+11)(2x-1); 1h) (3x+5)(x-4); 2a) 2(7x-5)(x+1); 2b) 3(3x-5)(x+1); 2c) 2x(7x-2)(x+5); 2d) 5x(5x+2)(x-1); 2e) y2(x+5)(4x-21); 2f) (4x-3t)(3x-4t); 2g) (-7x+2)(x+5); 2h) 3x2(6x-7)(x+1); 2i) x(2x2+5y2)(x2-3y2), 3a) (x+1)2, 3b) (2x-3)2, 3c) (5x+6y)2 3d) x(4x-y)2, 3e) 5x(x-1)2, 3f) 2a(1-6y)2