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

2023
Views:

418

Pages:

1
Author:

ui4s3l4md25

Mini-Lecture 6.2 Factoring Trinomials of the Form x2 + bx + c Learning Objectives: 1. Factor trinomials of the form x2 + bx + c. 2. Factor out the greatest common factor and then factor a trinomial of the form x2 + bx + c. Examples: 1. Factor each trinomial completely. If a polynomial can’t be factored, write “prime”. a) x2 + 11x + 30 b) y2 + 7y + 10 c) x2 + 3x – 4 d) x2 – 4x – 21 e) x2 – 13x + 30 f) x2 – x + 32 g) m2 + 17m + 16 h) 5x – 14 + x2 i) a2 + 13ab + 40b2 2. Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don’t forget to factor out the GCF first. a) 2x2 – 18x + 28 b) 3x2 + 6x – 9 c) x2 + 10x + 24 d) 2x2 + 20x – 22 e) 5x2 + 20x + 15 f) − x 3 + 3 x 2 + 10 x g) 4x4 – 36x3 + 56x2 h) x3y+ 10x2y2 + 24xy3 i) 1 2 8 y − y − 11 3 3 Teaching Notes: • • • • • • When factoring trinomials of this form, many students find it helpful to make a table listing all possible factor pairs for c in the first column and their sums in the second column. Some students have trouble factoring a trinomial when the last term is negative. Remind students that when the last term (the constant) of a trinomial is positive, the factors have the same sign. When the last term (the constant) of a trinomial is negative, the factors have different signs. Refer students to: To Factor a Trinomial of the Form x2 + bx + c in the textbook. Remind students that they can always check their work by multiplication. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) (x+6)(x+5); 1b) (y+5)(y+2); 1c) (x+4)(x-1); 1d) (x-7)(x+3); 1e ) (x-10)(x-3); 1f) prime; 1g) (m+16)(m+1); 1h) (x+7)(x-2); 1i) (a+8b)(a+5b); 2a) 2(x-7)(x-2); 2b) 3(x+3)(x-1); 2c) (x+6)(x+4); 2d) 2(x+11)(x-1); 2e) 5(x+3)(x+1); 2f) -x(x-5)(x+2); 2g) 4x2(x-7)(x-2); 2h) xy(x+6y)(x+4y); 2i) 1 ( y − 11)( y + 3) 3