Solving Quadratic Equations by Factoring MATH 018 Combined Algebra S. Rook

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

Solving Quadratic Equations by Factoring

4 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?

5 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?

6 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 7

8 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)6x 2 – x – 1 = 0 b)x 2 + 4x – 12 = 0 9

Zero Product Property – Not Factored (Example) Ex 3: Solve: a)x 2 = 8x – 15 b)x 3 = 25x c)x 3 + 3x 2 = 28x 10

Zero Product Property – Not Factored (Example) Ex 4: Solve: a)(5x + 2)(2x + 1) = 3 b)(3x + 2)(3x – 2) = 12 11

12 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)