Using Factoring To Solve

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Presentation transcript:

Using Factoring To Solve Section 8.5 Using Factoring To Solve Polynomial Equations

Zero Factor Property Property Let A and B be real number: If AB = 0, then A = 0 or B = 0. In words: If the product of two numbers is zero, then at least one of the numbers must be zero.

Solving Quadratic Equations in One Variable Solving a Quadratic Equation Example Solve (x – 5)(x + 2) = 0.

Solving Quadratic Equations in One Variable Solving a Quadratic Equation Solution

Solving Quadratic Equations in One Variable Solving a Quadratic Equation Example Solve w2 – 2w – 8 = 0.

Solving Quadratic Equations in One Variable Solving a Quadratic Equation Solution

Find the x-intercepts of the graph of f(x) = x2 – 7x + 10. Connection Between x-intercepts of a Quadratic Function Finding x-intercepts of a Quadratic Function Example Find the x-intercepts of the graph of f(x) = x2 – 7x + 10.

Check with a graphing calculator Connection Between x-intercepts of a Quadratic Function Finding x-intercepts of a Quadratic Function Solution Check with a graphing calculator

Solving More Quadratic Equations Solving Quadratic Equations Example Solve. 1. 4x2 + 26x + 30 = 0. 2. x2 – 10x + 25 = 0.

Solving More Quadratic Equations Solving Quadratic Equations Solution 1.

Solving More Quadratic Equations Solving Quadratic Equations Solution Continued 2.

Solving More Quadratic Equations Solving Quadratic Equations Rule The solution set of a quadratic equation in one variable may contain two real numbers, one real number, or no real numbers.

Solving More Quadratic Equations Solving Quadratic Equations Example Solve 2x2 – 8x = 5x – 20.

Solving More Quadratic Equations Solving Quadratic Equations Solution

Solving More Quadratic Equations Solving a Quadratic Equation That Contains Fractions Example Solve 1/2t2 + 1/3 = 5/6t

Solving More Quadratic Equations Solving a Quadratic Equation That Contains Fractions Solution

Solving More Quadratic Equations Solving a Quadratic Equation That Contains Fractions Solution Continued Example

Cubic Equations in One Variables Solving a Cubic Equation Example Solve 2x3 = 42x + 8x2.

Cubic Equations in One Variables Solving a Cubic Equation Solution

Cubic Equations in One Variables Solving a Cubic Equation Process If an equation can be solved by factoring, we solve it by the following steps: 1. Write the equation so that one side of the equation is equal to zero. 2. Factor the nonzero side of the equation. 3. Apply the zero factor property. 4. Solve each equation that results from applying the zero factor property.

Find the x-intercept of the graph of f(x) = x3 – 5x2 – 4x + 20. Cubic Equations in One Variables Finding x-intercepts of the graph of a Cubic Function Example Find the x-intercept of the graph of f(x) = x3 – 5x2 – 4x + 20. Solution

Use graphing to solve x2 – x – 7 = – x2. Solving Polynomial Equations in One Variable by Graphing Using Graphing to Solve an Equation in One Variable Example Use graphing to solve x2 – x – 7 = – x2.

Solution Use “intersect” on a graphing calculator to find solutions Solving Polynomial Equations in One Variable by Graphing Using Graphing to Solve an Equation in One Variable Solution Use “intersect” on a graphing calculator to find solutions Approx. Solution (–1.64, –2.68) and (2.14, –4.57)