1. Solve equations by factoring.
CHAPTER 8.5
Solve equations by factoring.

2. Principal of Zero Products
If the product of two factors is zero, then at least one of the factors must be zero.
If (a)(b)=0, then a=0 or b=0

3. Quadratic Equations Are equations in the form of ax2+bx+c=0, a=0.
A quadratic equation is in standard form when written in descending order and set equal to zero.

4. Solve (x-2)(x-3)=0 If (a)(b)=0, then a=0 or b=0
So, either x-2=0 or x-3=0
What number makes x-2=0 a true statement: x=2.
What number makes x-3=0 a true statement: x=3.
Or solve for x-2 = x-3 = 0
x = x = 3

5. Solve 2x2+x=6 Write the equation in standard form. 2x2+x-6=0.
Factor by preferred method.
2x2+x-6=0
(2x-3)(x+2)= 0
2x-3= 0 or x+2= 0
Solve for x
2x=3
x= 3
x=-2 .
Check by substitution.

6. Solve 2x2-50=0 Factor GCF 2(x2-25)=0 Continue factoring 2(x-5)(x+5)=0
2=0 or x-5=0 or x+5=0
Solve for x in each case.
2= x=5 or x=-5
Solutions x = -5,5
2 is not a solution.
Check by substitution.

7. Solve (x-3)(x-10)=-10
To set up as a Quadratic Equation, FOIL the left side of equation and then add ten to both sides x2-13x+40=0
Factor (x-5)(x-8)=0
Either x-5=0 or x-8=0
Solutions are
x=8,5
Check by substitution.

8. Solve (x+2)(x-7)=52
To set up as a Quadratic Equation, FOIL the left side of equation and then subtract 52 from both sides x2-5x- 66=0
Factor (x+6)(x-11)=0
Either x+6=0 or x-11=0
Solutions are
x=-6,11
Check by substitution.

9. NOW YOU TRY! 1. 3x(x-4)=0 4,0 2. 16x2-4=0 -1 , 1 2 2 3. x2-6x=7 -1,7
-1 , 1
3. x2-6x=7
-1,7
4. (x+3)(x-5)=9
-4, 6