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Bellwork Write the equation of the graph below in factored form.

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**Bell work Identify the type of polynomial**

Identify the number of solutions Identify the type of solutions (Classify)

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**7.5 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.

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**Rules and Properties Complex Conjugate Theorem**

7.5 Zeros of Polynomial Functions Rules and Properties Complex Conjugate Theorem If P is a polynomial function with real-number coefficients and a + bi is a root (zero). then a – bi is also a root (zero).

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**Rules and Properties Rational Root Theorem**

7.5 Zeros of Polynomial Functions Rules and Properties Rational Root Theorem P is a polynomial function with integer coefficients. If is a root of P(x) = 0, then p q p is a factor of the constant term of P. q is a factor of the leading coefficient of P.

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Example 1 Using the Rational Root Theorem, list all the POSSIBLE roots of the polynomial below.

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Problem 1 Using the Rational Root Theorem, list all the POSSIBLE roots of each polynomial below.

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Problem 3 Find all roots to the polynomial equation below.

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**7.5 Zeros of Polynomial Functions**

Problem 2 Write the equation for a third degree polynomial whose zeros are listed below and P(0) = -6 in factored & standard form.

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**7.5 Zeros of Polynomial Functions**

Example 2 Write the equation for a third degree polynomial whose zeros are 2 and i and P(0) = 4 in both factored & standard form.

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Problem 4 According 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.

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Homework 7.5: P even, odd, 41-43all, 47 (graphing calculator, synthetic division and factoring. You must show work. Test Tuesday- We have a no calc portion.

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