Write a polynomial function with given zeros and multiplicity
From: Brady T.
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Students will determine the multiplicity of zeros of a polynomial function when given its graph or its equation in factored form. Students will write an equation for a polynomial function when given information about its zeros and the multiplicity of the zeros. Students will write an equation for a polynomial function when given its graph. In this lesson, students utilize graphs and equations of five polynomial functions to determine the zeros of these five functions and whether the functions cross the x-axis or just touch the x-axis at the zeros. As a result, students will: Determine the degree of the polynomial functions and the effect the degree has upon the end behavior of the functions. Write possible equations for a polynomial function when given information about its zeros.
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How do you write a polynomial in standard form given zeros 1 (multiplicity 2), -2 (multiplicity 3)?
Zeros and multiplicity | Polynomial functions (article) | Khan Academy
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3.5: Zeros of Polynomial Functions
The Rational Zero Theorem helps us to narrow down the list of possible rational zeros for a polynomial function. Once we have done this, we can use synthetic division repeatedly to determine all of the zeros of a polynomial function. These are the possible rational zeros for the function. We will use synthetic division to evaluate each possible zero until we find one that gives a remainder of 0. The quadratic is a perfect square.
The fundamental theorem states that every non-constant, single-variable polynomial with complex coefficients has at least one complex root. As it turns out, every polynomial with a complex coefficient has a complex zero. Every polynomial of odd degree with real coefficients has a real zero.
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