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Solving Equations by Factoring

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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

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