Solving Quadratic Equations by Factoring

MATH 018

Combined Algebra

S. Rook

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Overview

• Section 6.6 in the textbook:– Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring

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Quadratic Equation - Definition

• Up to now, we have studied polynomial expressions– No =

• Quadratic Equation: a polynomial equation of degree 2

• Recall that we previously covered linear equations– What is the difference between a linear and a

polynomial equation?

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Zero Factor Property

• Zero Factor Property: If a ∙ b = 0, then either a = 0 or b = 0– Holds for real numbers or factors

• Notice that the Zero Factor Property only applies to a polynomial equation written as products

• What method can be used to transform a polynomial into products?

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Zero-Factor Property – Polynomial Already Factored

• Set each factor to 0 and solve for the variable– Apply the Zero-Factor Property

• Write the answer as a solution set

Zero Product Property – Polynomial Already Factored (Example)

Ex 1: Solve:

a) (2x – 9)(x + 4) = 0

b) (5x + 3)(x – 1) = 0

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Zero-Factor Property – Not Factored

• Move all terms from one side to the other– i.e. set one side to zero– Easiest to work with when the coefficient of

the squared term is positive

• Factor using the strategies that we have discussed

• Apply the Zero-Factor property

• Write the answer as a solution set

Zero Product Property – Not Factored (Example)

Ex 2: Solve:

a) 6x2 – x – 1 = 0

b) x2 + 4x – 12 = 0

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Zero Product Property – Not Factored (Example)

Ex 3: Solve:

a) x2 = 8x – 15

b) x3 = 25x

c) x3 + 3x2 = 28x

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Zero Product Property – Not Factored (Example)

Ex 4: Solve:

a) (5x + 2)(2x + 1) = 3

b) (3x + 2)(3x – 2) = 12

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Summary

• After studying these slides, you should know how to do the following:– Solve quadratic equations by factoring

• Additional Practice– See the list of suggested problems for 6.6

• Next lesson– Quadratic Equations and Problem Solving

(Section 6.7)