Algebra 2 Lesson 7.3 Solving Equations Using Quadratic Techniques Objectives: •
Factoring and zero product Property.
•
Write a polynomial function in quadratic form and solve.
Technique 1: Factoring and zero product property.
Zero Product Property:
( x ! a )( x ! b ) = 0 …
If you have an equation, first set it equal to zero, 2nd factor, then use the zero product property to solve. Factoring ways: GCF, ac method, grouping, and use special forms like x 3 ! y 3 = ( x ! y ) ( x 2 + xy + y 2 ) … Example 1:Solve each equation a. x 5 + 6x 4 + 5x 3 = 0
b. x 3 + 8 = 0
c. b 4 = 16
d. m 3 + 4m 2 ! m ! 4 = 0
Technique 2: Write a polynomial function in quadratic form and solve using the quadratic formula. Example 2: Write in quadratic form and solve each equation a.
x 4 ! 11x 2 + 18 = 0
1 2
b. y ! 19y = !60
c.
2 3
1 3
p + 11p + 28 = 0
HW: Section 7-3, page 363 #s 7,9, 17-27odd P. 842 Section 7.3: 11-23 odd, opt: 10, 20