Presentation on theme: "Bellwork Write the equation of the graph below in factored form."— Presentation transcript:
1BellworkWrite the equation of the graph below in factored form.
2Bell work Identify the type of polynomial Identify the number of solutionsIdentify the type of solutions (Classify)
37.5 Zeros of Polynomial Functions Students will be able to:Use the Rational Root Theorem and the Complex Conjugate Root Theorem to find the zeros of a polynomial function.Use the Fundamental Theorem to write a polynomial function given sufficient information about its zeros.
4Rules and Properties Complex Conjugate Theorem 7.5 Zeros of Polynomial FunctionsRules and PropertiesComplex Conjugate TheoremIf P is a polynomial function with real-number coefficientsand a + bi is a root (zero).then a – bi is also a root (zero).
5Rules and Properties Rational Root Theorem 7.5 Zeros of Polynomial FunctionsRules and PropertiesRational Root TheoremP is a polynomial function with integer coefficients.If is a root of P(x) = 0, thenpqp is a factor of the constant term of P.q is a factor of the leading coefficient of P.
6Example 1Using the Rational Root Theorem, list all the POSSIBLE roots of the polynomial below.
7Problem 1Using the Rational Root Theorem, list all the POSSIBLE roots of each polynomial below.
8Problem 3Find all roots to the polynomial equation below.
97.5 Zeros of Polynomial Functions Problem 2Write the equation for a third degree polynomial whose zeros are listed below and P(0) = -6 in factored & standard form.
107.5 Zeros of Polynomial Functions Example 2Write the equation for a third degree polynomial whose zeros are 2 and i and P(0) = 4 in both factored & standard form.
11Problem 4According to the Fundamental Theorem of Algebra, what can I conclude about the polynomial below?2. Given -6 as a root of the polynomial above, find the remaining roots.
12Homework7.5: P even, odd, 41-43all, 47 (graphing calculator, synthetic division and factoring. You must show work.Test Tuesday- We have a no calc portion.