About Solving Quadratic Equations by Factoring:
A quadratic equation in standard form: ax2 + bx + c = 0. a, b, and c are real numbers, a ≠ 0. When the left side is factorable, we simply factor the left side and set each factor with a variable equal to zero. We then solve the resulting equations and check our solutions.
Test Objectives
- Demonstrate the ability to factor a trinomial
- Demonstrate the ability to use the zero-product property
- Demonstrate the ability to check the proposed solutions for an equation
#1:
Instructions: Solve each equation by factoring.
a) $$v^{2} - 4v - 5 = 0$$
b) $$b^{2} - 2b + 1 = 0$$
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#2:
Instructions: Solve each equation by factoring.
a) $$v^{2} + 40 = 13v$$
b) $$k^{2} + 10 = -7k$$
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#3:
Instructions: Solve each equation by factoring.
a) $$7x^{2} = 28x - 28$$
b) $$5a^{2} = 15a$$
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#4:
Instructions: Solve each equation by factoring.
a) $$6x^{2} + 23 = 19x + 8$$
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#5:
Instructions: Solve each equation by factoring.
a) $$19x^{2} - 180x - 160 = -6x^{2}$$
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Written Solutions:
#1:
Solutions:
a) $$v = 5, -1$$
b) $$b = 1$$
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#2:
Solutions:
a) $$v = 8, 5$$
b) $$k = -5, -2$$
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#3:
Solutions:
a) $$x = 2$$
b) $$a = 0, 3$$
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#4:
Solutions:
a) $$x = \frac{3}{2}, \frac{5}{3}$$
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#5:
Solutions:
a) $$x = -\frac{4}{5}, 8$$
