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Solving Quadratic Equations
By Factoring
Medina
1
Solving Quadratic Equations
by factoring
Step 1: Write equation in
Example:
Standard Form
x² + 4x + 3 = 0
Ax² + Bx + C = 0
Step 2: Using factoring rules to
factor
GCMF
Diamond
Step 3: Using the zero product
property to solve
Solving Quadratic Equations
by factoring
Solve:
GCMF
Diamond

x  x 6  0
2
1. Equation is already
in Standard Form
( x  2)( x  3)  0
Solving Quadratic Equations
by factoring
Step 3: Solve for x using the zero
product property
( x  2)( x  3)  0
x2  0
2 2
x2
x3  0
3 3
x  -3
Solving Quadratic Equations
by factoring
x  7 x  12  0
2
( x  3)( x  4)  0
x3  0
3  3
x  -3
x40
4 4
x  -4
Solving Quadratic Equations
by factoring
x  3x  10  0
2
( x  2)( x  5)  0
x2  0
2  2
x2
x5  0
5 5
x  -5
Solving Quadratic Equations
by factoring
x  5 x  6
6 6
2
x  5x  6  0
( x  2)( x  3)  0
2
x20
2  2
x  2
x3  0
3  3
x  3
Solving Quadratic Equations
by factoring
x( x  6)  27
x  6 x  27
27  27
2
x  6 x  27  0
( x  9)( x  3)  0
2
x 9  0
9  9
x9
x3  0
3  3
x  3
Solving Quadratic Equations
by factoring
CW Problem # 15
Area = l w
Area = 21in²
Area = x(x+4)
21 = x(x+4)
But distance can
only be positive,
therefore x =3
21  x  4 x
21
 21
2
0  x  4 x  21
( x  3)( x  7)  0
2
x 3  0 x  7  0
 3  3 7  7
x3
x  7