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Quadratic Equations: Factoring Test
About Solving Quadratic Equations by Factoring:

A quadratic equation in standard form: ax2 + bx + c = 0. a, b, & 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 results.

Test Objectives:

•Demonstrate the ability to factor a polynomial

•Demonstrate the ability to use the zero product property

•Demonstrate the ability to check the proposed solutions for a quadratic equation

Solving Quadratic Equations by Factoring Test:




#1:


Instructions: Solve each quadratic equation by factoring.


a) v2 - 4v - 5 = 0


b) b2 - 2b + 1 = 0


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#2:


Instructions: Solve each quadratic equation by factoring.


a) v2 + 40 = 13v


b) k2 + 10 = -7k


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#3:


Instructions: Solve each quadratic equation by factoring.


a) 7x2 = 28x - 28


b) 5a2 = 15a


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#4:


Instructions: Solve each quadratic equation by factoring.


a) 6x2 + 23 = 19x + 8


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#5:


Instructions: Solve each quadratic equation by factoring.


a) 19x2 - 180x - 160 = -6x2


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Written Solutions:




#1:


Solution:


a) v = 5 or v = -1


b) b = 1


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#2:


Solution:


a) v = 8 or v = 5


b) k = -5 or k = - 2


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#3:


Solution:


a) x = 2


b) a = 0 or a = 3


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#4:


Solution:


a)


x =  3  or  x =  5
2 3

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#5:


Solution:


a)


x =  -4  or  x = 8
 5

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