2. Problem: y=(x+2)(x-3) FOIL (first - outer - inner - last) y=x 2 -3x +2x-6 Reduce: y=x 2 -x-6 Graph

3. Factoring a Trinomial of the Form x^2+bx+c Factor: x 2 -12x-28 Solution: You want x 2 -12x-28=(x+m)(x+n) where mn=-28 and m+n=-12 The table shows that m=2 and n=-14. x 2 – 12x – 28 (x+2)(x-14)

4. Solving A Quadratic Equation Solve: (x+3) 2 =7 Solution: (x+3) 2 =7 Write original equation. (x+5) 2 =21 Multiply each side by 3. x+5= Take square roots of each side. x= -5 Subtract 5 from each side. The solutions are 5 + and -5 -.

5. Solving a Quadratic Equation Solve: 3x 2 +10 = -26 Solution: 3x 2 +10 = -26 Write original equation. 3x 2 = -36 Subtract 10 from each side. X 2 = -12 Divide each side by 3. X = Take square roots of each side. X = Write in terms of i. X = Simplify the radical. The solutions are and

6. Solving a Quadratic Equation if the Coefficient of x 2 is 1 Solve x 2 +10x-3 = 0 by completing the square. Solution: x 2 +10x-3 = 0 Write the original equation. x 2 +10x = 3 Write the left side in the form x2 + bx. x 2 +10x+52 = 3+25 Add 2 = 5 2 = 25 to each side. (x+5) 2 = 28 Write the left side as a binomial squared. x+5 = Take square roots of each side. x = -5 Solve for x. x = -5 Simplify. The solutions are -5 + and -5 -.