1. 8-6 Solving Polynomial equations in factored form
Goals:
Solve a polynomial equation in factored form
Relate factors and x-intercepts.
Eligible Content: A

2. Vocabulary
Factored Form – the product of two or more linear polynomials.
Linear – biggest exponent is one.
Zero-Product Property – If two things multiply together to make zero, one or both must be zero.

3. Solve the Equation (x – 2)(x + 3) = 0 x – 2 = 0 x + 3 = 0 +2 +2 -3 -3
x = 2
x = -3
x = 2 or -3

4. Examples (x + 5)(x – 7) = 0 (x – 10)(3x – 9) = 0 4(x + 1)(x + 3) = 0
x = -5/3, ¾ and 3

5. Solve (s – 3)(3s + 6) = 0. Then check the solution.
A. {3, –2}
B. {–3, 2}
C. {0, 2}
D. {3, 0}

6. Practice (x + 3)(x + 6) = 0 3(x – 4)(2x + 8) = 0 (x + 12)(x – 5) = 0
x = 7, -7 and 4

7. Let’s look at the graphs!!
Use your calculator to look at the graphs of the equations.
Parabola – the shape that is created by the quadratic equation.
The x-intercepts of the graph are the solutions to the equation. These are also called ZEROS.

8. Graph the problems we solved earlier.
(x + 5)(x – 7) = 0
(x – 10)(3x – 9) = 0
4(x + 1)(x + 3) = 0
(x + 7)2 = 0
(2x + 12)(x – 8)(3x + 3) = 0
5(3x + 5)(4x – 3)(6x – 18) = 0
x = -5 & 7
x = 10 & 3
x = -1 & -3
x = -7
x = -6, 8 &-1
x = -5/3, ¾ and 3
The solutions are the
x-intercepts of the graph!!!

9. Homework
Worksheet – “Solving Polynomial Equations in Factored Form Homework”