advertisement

Factor and Solve Polynomial Equations-- Notes Consider the following: ab=0 Question: If I multiply two things together and the result is zero, what can I say about those two things? Answer: The only way to multiply and get zero is to multiply by _______. This is called "The ______________________ Property" Let's apply this property to some factors: (x – 3)(x – 4) = 0 (x + 2)(x + 3) = 0 x(x + 5) = 0 8x(x + 2) = 0 (2x – 3)(x + 1) = 0 5(x – 7)(x + 10)=0 Two types of polynomial equations: Quadratic Equation Binomial Equation 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 𝒂𝟐 − 𝒃𝟐 = 𝟎 Factor Set each factor equal to zero Solve each factor for the variable Solutions: Find the solutions of each polynomial. 1. x2 − 4x − 5 = 0 Roots: 2. 0 = 4x2 + 9x + 5 3. 2𝑥 2 + 6𝑥 = 0 Find the roots of each function.(Set equal to 0 by replacing f(x)) 3. f(x) = 3x2 + 2x − 8 4. f(x) = x2 − 64 5. 𝑓(𝑥) = 10𝑥 2 − 5𝑥 Summarize: 5x2 + 28x − 12 = 0 (5x−2)(x+6) =0 x= { 2 5 , -6} If you know your solutions/roots, you can find the factors of the polynomial: Start your parenthesis (x )(x Solutions/Roots ) Switch the sign of each root and plug it into your parenthesis Factors: 12, 7 -5, -10 3, -1 2 3 ,5 −1 2 ,4 20, 6 4 -4, 3 If there is a denominator, slide it in front of your variable