8-6 Solving Polynomial equations in factored form Goals: Solve a polynomial equation in factored form Relate factors and x-intercepts. Eligible Content: A1.1.1.5.2

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.

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

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

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

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

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.

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!!!

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