Intermediate Algebra – Student Workbook – Second Edition 2013

Lesson 5b - Solving Quadratic Equations
Mini-Lesson
Problem 3
WORKED EXAMPLE – SOLVE QUADRATIC EQUATIONS BY
FACTORING (GCF)
Use the method discussed on the previous page, Factoring using the GCF, to solve each of the
quadratic equations below. Verify your result by graphing and using the Intersection method.
a) Solve by factoring: 5x 2 - 10x = 0
One way you can recognize that GCF is a good method to try is if you are given 2 terms
only (called a BINOMIAL). This will be more important when we have other factoring
methods to try and quadratics with more terms.
Step 1: Make sure the quadratic is in standard form (check!).
Step 2: Check if there is a common factor, other than 1, for each term (yes…5x is
common to both terms)
Step 3: Write the left side in Completely Factored Form
5x 2 - 10x = 0
(5x)(x - 2) = 0
Step 4: Set each linear factor to 0 and solve for x:
5x = 0 OR x – 2 = 0
x = 0 OR x = 2
Step 5: Verify result by graphing (Let Y1 = 5x 2 - 10x, Y2 = 0, zoom:6 for standard
window then 2 nd >Calc>Intersect (two separate times) to verify solutions are x =
0 and x = 2).
Step 6: Write final solutions (usually separated by a comma): x = 0, 2
b) Solve by factoring: -2x 2 = 8x
Step 1: Make sure the quadratic is in standard form (need to rewrite as -2x 2 - 8x = 0)
Step 2: Check if there is a common factor, other than 1, for each term (yes…-2x is
common to both terms – note that you can also use 2x but easier to pull the
negative out with the 2x)
Step 3: Write the left side in Completely Factored Form
-2x 2 - 8x = 0
(-2x)(x + 4) = 0
Step 4: Set each linear factor to 0 and solve for x:
-2x = 0 OR x + 4 = 0
x = 0 OR x = -4
Step 5: Verify result by graphing (Let Y1 = -2x 2 - 8x, Y2 = 0, zoom:6 for standard
window then 2 nd >Calc>Intersect (two separate times) to verify solutions are x =
0 and x = -4).
Step 6: Write final solutions (usually separated by a comma): x = 0, -4
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