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Solving Equations by Factoring

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**3. **Standard Form Quadratic Equation Quadratic equations can be written in the form
ax2 + bx + c = 0
where a, b, and c are real numbers with a ? 0.

**4. **Examples of Quadratic Equations

**5. **Zero-Factor Property If a and b are real numbers
and if ab =0, then
a = 0 or
b = 0.

**6. **Solve the equation (x + 2)(2x - 1)=0 By the zero factor property we know...
Since the product is equal to zero then one of the factors must be zero.

**7. **Solve the equation. Check your answers.

**8. **Solve each equation. Check your answers.

**9. **Solving a Quadratic Equation by Factoring Step 1 Write the equation in standard form.
Step 2 Factor completely.
Step 3 Use the zero-factor property. Set each factor with a variable equal to zero.
Step 4 Solve each equation produced in step 3.

**10. **Solve.

**11. **Solve.

**12. **Solve.

**13. **Number Of Solutions The degree of a polynomial is equal to the number of solutions.

**14. **Example x (x + 1)(x – 3) = 0
Set each of the three factors equal to 0.

**15. **Solve.

**16. **Example: x2 – 9x + 20 = 0
(x – 4)(x – 5) = 0
x – 4 = 0
x = 4
x – 5 = 0
x = 5
x = {5, 4} Standard form already
Factor
Set each factor = 0
Solve
Write the solution set

**17. **Example 4x2 – 49 = 0
(2x + 7)(2x – 7) = 0
2x + 7 = 0
2x – 7 = 0 Standard form already
Factor
Set each factor = 0
Solve
Write the solution set