Use the resources on the internet and each other to help you relearn the concept. Use whiteboards. Use laptops. Work together.

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Presentation transcript:

Use the resources on the internet and each other to help you relearn the concept. Use whiteboards. Use laptops. Work together.

We will be reviewing our previous assignment next. So have your questions ready.

SWBAT write a polynomial function given the real and complex zeros. Write down the date, Section #, Title and Learning Objective(s) into your notebook.

LOOK LISTEN Write down what you want into Key Concepts as you Look & Listen. Complex Number Factoids: Difference of Squares:

LOOK LISTEN Write down what you want into Key Concepts as you Look & Listen. Linear Factorization Theorem If f(x) is a polynomial of degree n where n>0, f has precisely n linear factors. Where c 1, c 2, … c n are complex numbers.

LOOK LISTEN Write down what you want into Key Concepts as you Look & Listen. Linear Factorization Theorem Example This is a second degree polynomial and therefore must have precisely 2 complex zeros. After factoring, we can see that the zero is 3 and is repeated twice. i.e. it has a multiplicity of 2. How would the graph intersect at this zero? How do you know?

LOOK LISTEN Write down what you want into Key Concepts as you Look & Listen. Linear Factorization Theorem Example This is a second degree polynomial and therefore must have precisely 3 complex zeros. After factoring, we can see that the zeros are {0, +2i, -2i}. How many intersection points would the graph have on the x-axis? Why?

LOOK LISTEN Write down what you want into Key Concepts as you Look & Listen. If I am given the zeros, how do I find the polynomial? Take each zero and replace in the Linear Factorization Theorem.

SWBAT write a polynomial function given the real & complex zeros. LOOK LISTEN Find a 2 nd degree polynomial that has the given zeros of: {-4, 7}.

Use whiteboards. SWBAT write a polynomial function given the real & complex zeros. Find a 3 rd degree polynomial that has the given zeros of: {0, 1, -2}.

Use whiteboards. SWBAT write a polynomial function given the real & complex zeros. Find a 2 nd degree polynomial that has the given zeros of: {-5 with multiplicity of 2}.

Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 3 rd degree polynomial that has the given zeros of: {0 with multiplicity of 2, -1}.

LOOK LISTEN SWBAT write a polynomial function given the real & complex zeros. Find a 2 nd degree polynomial that has the given zeros of:. * Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.

Use whiteboards. SWBAT write a polynomial function given the real & complex zeros. Find a 4 th degree polynomial that has the given zeros of:. * Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.

Use whiteboards. SWBAT write a polynomial function given the real & complex zeros. Find a 3 rd degree polynomial that has the given zeros of:. * Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.

Use whiteboards. SWBAT write a polynomial function given the real & complex zeros. Find a 5 th degree polynomial that has the given zeros of:. * Complex numbers ALWAYS come in pairs. i.e. a+bi and a-bi.

Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 4 th degree polynomial that has the given zeros of:.

Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 2 nd degree polynomial that has the given zeros of:.

Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 4 th degree polynomial that has the given zeros of:.

Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 4 th degree polynomial that has the given zeros of:.

Write in notebook. SWBAT write a polynomial function given the real & complex zeros. Find a 2 nd degree polynomial that has the given zeros of:.

Write a polynomial function with real coefficients that has the given zeros: