Polynomials Integrated Math 4 Mrs. Tyrpak. Definition.

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Presentation transcript:

Polynomials Integrated Math 4 Mrs. Tyrpak

Definition

Key Terms

You try one…

Relationships?

The Leading Coefficient Test L.C. EVEN ODD Same Different L.C. DEGREE

Real Zeros The following are equivalent statements about real zeros of a polynomial function: 1.x = a is a zero (solution or root) of the function 2.(a, 0) is an x-intercept of the graph 3.(x – a) is a factor of the polynomial

Finding All Zeros

Rational Zeros Theorem

Synthetic Division Second, we are going to use synthetic division to test each possible zero.

The Remainder and Factor Theorems Remainder Theorem: If a polynomial f(x) is divided by x – k, the remainder is r = f(k). Factor Theorem: A polynomial f(x) has a factor (x - k) if and only if f(k)=0.

Factor the Polynomial

Find all the zeros Lastly, we will solve each factor for each zero.

Fundamental Theorem of Algebra If f(x) is a polynomial of degree n, where n > 0, f has at least one zero in the complex number system.

Multiplicity

Find the zeros of the polynomial function and state the multiplicity of each and what happens at each zero.

Finding All Zeros and Factors

Take 5 minutes and try this one..

Let’s try and work backwards Find a polynomial with integer coefficients that has the given zeros: 1, 5i, -5i

Thanks for your attention! Don’t forget to complete both the extension and enrichment assignments before you move on. Keep up the hard work!