Warmup Solve –2x2 + 5x = 0. Approximate non-integral answers. A. 0 B. 0, 2.5 C. 1.5 D. 2, –2

3-4 Solving Quadratic Equations by factoring Write quadratic equations in standard form. Solve quadratic equations by factoring.

Writing a quadratic Equation 19. Write a quadratic equation in standard form with root(s) 1 5 , 6

Standard Form 𝑎 𝑥 2 +𝑏𝑥+𝑐=0 Really called the distributive property!

Factor each polynomial Let’s recall a few factoring rules! 𝑃𝑒𝑟𝑓𝑒𝑐𝑡 𝑆𝑞𝑢𝑎𝑟𝑒 𝑡𝑟𝑖𝑛𝑜𝑚𝑖𝑎𝑙𝑠 𝑎+𝑏 2 = 𝑎 2 +2𝑎𝑏+ 𝑏 2 𝑎−𝑏 2 = 𝑎 2 −2𝑎𝑏+ 𝑏 2 𝑆𝑢𝑚 𝑎𝑛𝑑 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑎+𝑏 𝑎−𝑏 = 𝑎 2 − 𝑏 2 ?????= 𝑎 2 + 𝑏 2 Factor out any greatest common factor GCF. Write in front of parenthesis If coefficient of the x2 term is one, figure out two numbers that when multiplied give you the constant and when added give you the coefficient of the x term. If coefficient of the x2 term is not one, use x-Group factoring.

Factor 27. 𝑥 2 − 9𝑥 − 22

Factor

Factor First, factor out any common factors and put in standard form. With what is left: Draw a large x Put acx2 in the top part Put bx in the bottom part Find two terms that multiply to give you acx2 and add to give you bx. Place those two quantities in left and right side (any order). Rewrite the quadratic part by replacing middle term with the left and right 2 quantities.

Zero Product Property

Find x and the dimensions of the rectangle

Solve the equation 50. 5 𝑥 2 =15𝑥

Solve the equation by factoring