Factor: Factor: 1. s 2 r 2 – 4s 4 1. s 2 r 2 – 4s b b 3 c + 18b 2 c b b 3 c + 18b 2 c 2 3. xy + 3x – 2y xy + 3x – 2y - 6

Objective: To use factoring in solving polynomial equations

For all real numbers a and b: For all real numbers a and b: ab = 0 if either a = 0 or b=0 b=0

ax + b=0 Linear Equation ax 2 + bx + c =0 Quadratic Equation ax 3 + bx 2 +cx + d=0 Cubic Equation Parabola

The points where the parabola crosses the x axis are the ROOTS of the equation. The points where the parabola crosses the x axis are the ROOTS of the equation.

Many of the polynomial equations can be solved by factoring the polynomial and setting each factor equal to zero. Many of the polynomial equations can be solved by factoring the polynomial and setting each factor equal to zero. Solving each of those factors will give you the roots. Solving each of those factors will give you the roots.

x 2 + x – 12 = 0 x 2 + x – 12 = 0 Factor: (x – 3)(x + 4) =0 Factor: (x – 3)(x + 4) =0 Set equal to 0: x – 3= 0 x+ 4 = 0 Set equal to 0: x – 3= 0 x+ 4 = 0 Solve: x= 3 x= – 4 Solve: x= 3 x= – 4 Solution set: {3,-4} Solution set: {3,-4}

In this example, we still need to set the equation equal to zero before we can factor. In this example, we still need to set the equation equal to zero before we can factor. 5z 2 – 80 =0 5z 2 – 80 =0 5(z 2 – 16)= 0 5(z 2 – 16)= 0 5(z-4)(z+ 4) = 0 5(z-4)(z+ 4) = 0 z – 4= 0 z + 4 =0 z – 4= 0 z + 4 =0 z= 4 z = – 4 z= 4 z = – 4

6n n=10 6n n=10

18y 3 +66y 2 -24y = 0 18y 3 +66y 2 -24y = 0

6 b(b + 5)(b+2)=0 6 b(b + 5)(b+2)=0 s 2 = 18s – 81 s 2 = 18s – 81

8b 2 = 14b b 2 = 14b = 6x 3 -24x 0 = 6x 3 -24x