Solving Polynomial Equations in Factored Form Lesson 10.4A Algebra 2.

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Presentation transcript:

Solving Polynomial Equations in Factored Form Lesson 10.4A Algebra 2

Solving Factored Equations Factored Form of a Polynomial A polynomial that is written as the product of two or more prime factors.

Zero Product Property If ab = 0, then a = 0 or b = 0 for all real numbers a and b. The product of two factors is zero only when at least one of the factors is zero.

Using the Zero Product Property Solve the equation (x – 1)(x + 7) = 0

You try: Solve the equation (z – 6)(z + 6) = 0.

Try this one: Solve the equation (x – 4) 2 = 0 End of Lesson

Solving Polynomial Equations in Factored Form Lesson 10.4B Algebra 2

Relating Factors and X-intercepts You can use the zero product property to find the intercepts of an equation in factored form. This allows you to easily graph the equation. Step 1: Solve the equation using the zero product property. This gives you the x-intercepts of the graph. Step 2: Find the vertex. The x-coordinate of the vertex is the average of the x-intercepts. Step 3: Substitute the value of the x-coordinate into the original equation to find the value of the y-coordinate of the vertex.

Example: Graph the function: y = (x + 4)(x – 2)

You try: Find the x-intercepts and the location of the vertex. Then sketch a graph of the function. y = (x + 3)(x + 1) End of Lesson