Solving Quadratic Equations by Factoring
Standard form of a quadratic: 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0
Zero Product Property – if the product of two quantities equals zero, at least one of the
quantities must be zero
Steps to solving by factoring
1. Equation must be in standard form.
2x2 – 9x – 5 = 0
2. Factor using the box.
3. Set each (
) = 0.
4. Solve for “x” in each.
5. Check your answers.
A. 3x2 – x – 4 = 0
B. 4x2 + 20x + 25 = 0
C. 4x2 – 9 = 0
D. 2x2– 4x + 5 =0
Solving Quadratics Using the Quadratic Formula
The Quadratic Formula
b  b2  4ac
x
2a
Ex: Solve using the quadratic formula.
1. 3x2 + x – 10 = 0
2. 4x2 – 7x – 5 = 0
3. 8x2 + 6x – 5 = 0
Solving Quadratic Equations by Using Square Roots
x2 – 16 = 0
Steps:
1. Is there a bx term?
If not, you can use this method
2. Put the equation in x2 = c form
3. Square root both sides
4. Check
A. 4x2 – 25 = 0
B. x2 + 5 = 5
C. x2 = 20