1. Solving Quadratics by Factoring
By Anthony, Salma, Emily, & Henry

2. Definitions Binomials - an expression with 2 terms: x+3
Trinomials - an expression with 3 terms: x²+8x+19
Quadratic - x²+9 or x²+3x+19

3. (x+4)(x+3) Factoring allows you to find a solution for a trinomial.
We’re trying to find factors (a factor is something that can be multiplied by)
For example: x²+7x+12=0
(x+4)(x+3)
So the solutions will be x=-4 and x=-3

4. How to Factor -7+5=-2 -7×5=-35 So the factors will be (x-7)(x+5)=0
a+b= a×b=-35
Factors of: 35: 1,5,7,35
-7+5=-2 -7×5=-35
So the factors will be
(x-7)(x+5)=0

5. Quadratic Solution So now we have the factor (x-7)(x+5)=0
The Zero Factor Property tells us if
a × b = 0 then a = 0 or b = 0 (or both a=0 and b=0)
So you set them both equal to zero
x-7=0 x+5=0
Solve
Solutions for the quadratic equation is
x=7,-5

6. Checking Work
The solutions to quadratic equations may be verified by plugging them back into the original equation. This makes sure that they work and that they result in a true statement.
Checking 7 in x²-2x-35=0
(7)²-2(7)-35=0
Checking -5 in x²-2x-35=0
(-5)²-2(-5)-35=0
Equals zero
Equals zero

7. Now try this:
x²-16x+64=0
(x-8)²
x-8=0
x=8
x-8=0
x=8

8. Here’s another example:
x² +2x-3=0
(x+3)(x-1)
x+3=0
x=-3
x-1=0
x=1