5 2 Polynomial Linear Factors Learning goals graph

5. 2 Polynomial & Linear Factors Learning goals • graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases • graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior

Ex 1 Write in factored form, and then find the zeros.

The following are equivalent statements about a real number b and a polynomial P(x): • (x – b) is a factor of P(x) • b is a zero of the function • b is a root (or solution) of P(x) = 0 • b is an x-intercept of the graph

So, for example… Equivalent Statements about Polynomials • – 4 is a solution of • – 4 is an x-intercept of the graph • – 4 is a zero of • (x + 4) is a factor of

Ex 2 Find the zeros and graph

Ex 3 Find the zeros and graph

Ex 4 Write an equation in standard form with zeros at

Vocabulary multiple zero : a repeated zero of a polynomial that occurs because of a repeated linear factor multiplicity : the number of times a zero occurs in a polynomial

Ex 5 For the following polynomial, find any multiple zeros and state the multiplicity of each

Vocabulary relative minimum and relative maximum : peaks and valleys within the graph of a polynomial that has several turning points

Ex 5 Find the relative minimum and maximum