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

2023
Views:

64

Pages:

1
Author:

Kristopher Elliott

Mini-Lecture 6.6 Solving Quadratic Equations by Factoring Learning Objectives: 1. Solve quadratic equations by factoring. 2. Solve equations with degree greater than 2 by factoring. 3. Find the x-intercepts of the graph of a quadratic equation in two variables. Examples: 1. Solve each equation. a) (x – 1)(x + 4) = 0 b) (x + 5)(x + 9) = 0 c) (x – 10)(x + 8) = 0 d) 5x(x – 15) = 0 e) (2x – 5)(x + 3) = 0 2 ⎞⎛ 1⎞ ⎛ f) ⎜ x − ⎟⎜ x − ⎟ = 0 7 ⎠⎝ 3⎠ ⎝ g) x 2 − x − 30 = 0 h) x 2 − 9 x + 20 = 0 i) y 2 − y − 42 = 0 j) x 2 − 7 x = 0 k) x 2 = 25 l) x 2 + 2 x = 15 m) 5 x 2 − 30 x + 40 = 0 n) x( x − 4) = 21 o) x ( x − 6 ) = 16 2. Solve the following equations with degree greater than 2 by factoring. a) y 3 + 14 y 2 + 49 y = 0 b) 24 x3 − 4 x 2 − 20 x = 0 c) d) 16a3 − 9a = 0 e) 49t 3 − 4t = 0 f) ( x − 4 ) ( x 2 − 3x + 2 ) = 0 ( 9 x + 5) (10 x 2 − 3x − 4 ) = 0 3. Find the x-intercepts of the graph. a) y = ( x − 4)( x + 5) b) y = ( x − 1)( x + 1) c) y = x3 − x 2 − 4 x − 4 Teaching Notes: • • Remind students to always put the equation into standard form. Some students try to use the zero factor property before the equation is in standard form. For example 1n) x ( x − 4 ) = 21 → x = 21, x − 4 = 21, etc. • • Students will find this section challenging. Remind students to always check their answers. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. • Answers: 1a) 1, -4; 1b) -5, -9; 1c) 10, -8; 1d) 0, 15; 1e) 5/2, -3; 1f) 2/7, 1/3; 1g) 6, -5; 1h) 4, 5; 1i) 7, -6; 1j) 0, 7; 1k) 5, -5; 1l) -5, 3; 1m) 2, 4; 1n) 7, -3; 1o) –2, 8; 2a) 0, -7; 2b) 0, -5/6, 1; 2c) 4, 2, 1; 2d) 0, ¾, -3/4; 2e) 0, 2/7, -2/7; 2f) -5/9, -1/2, 4/5, 3a) (4,0), (-5,0), 3b) (1,0), (-1,0), 3c) (2,0), (-2,0), (1,0)