Polynomial Equations A polynomial equation is any equation that contains a polynomial expression. The degree of a polynomial equation is the degree of the polynomial expression in the equations. 2x2 + 5x + 3 = 0 is a second degree polynomial equation. The zero-product property states that if the product of two numbers is zero, then one of those numbers must be zero. If your answer to a multiplication problem is zero, then one of the numbers you are multiplying (factors) must be zero. A quadratic equation is an equation in the form ax2 + bx + c = 0 where a, b and c are real numbers and a 0. When it is written in descending order of exponent like this, it is said to be in standard form. Since the left-hand side is a 2nd degree polynomial, these are also sometimes known as second-degree equations. Steps for solving a quadratic equation by factoring 1. 2. 3. 4. 5. Make sure the polynomial is in standard form and equals zero. Factor the polynomial Set each of the factors equal to zero Solve those two little equations Check your answers by substituting back into the original. Remember: As soon as you see a square and an equal sign: Drag everything to the left and put the terms in order Expect 2 answers Solving higher order equations by factoring w3 + 5w2 – 4w – 20 = 0 3rd degree – expect 3 answers w2(w + 5) – 4(w + 5) = 0 (w + 5)(w2 – 4) = 0 (w + 5)(w + 1)(w – 1) = 0 w+5=0|w+1=0|w–1=0 w = -5 | w = -1 | w=1 Solving equations involving polynomial functions f(x) = x2 – 5x + 4 for what values of x does f(x) = 4? x2 – 5x + 4 = 4 x2 – 5x + 4 – 4 = 0 x2 – 5x = 0 x( x – 5) = 0 x=0|x–5=0 x=0| x=5 Finding the zeros of a function You are finding the values of x when y = 0. In other words, where the graph crosses the xaxis.