1. Suppose that a polynomial has a zero at 4 with a multiplicity of 3, a zero at -7 with a multiplicity of 5, and a zero at -4 with a multiplicity of 1. (A) Write a polynomial function in factored form that would have these zeros with their multiplicity. What is the degree of your polynomial function? Explain how you determined the degree. (B) Write a second polynomial function in factored form having the same zeroes and multiplicity as stated above, but with a different degree. State your new degree.

Describe the end behavior of each polynomial. (a) y=x38x2+2x15 End behavior: y as x y as x (b) y=2x4+12x+100 End behavior: y as x y as x

Given the following information about a polynomial function, find the function. It has a double zero at x=3 and zeroes at x=1 and x=2 It’s y-intercept is (0,12).

Find a fourth-degree polynomial function f with real coefficients that has 2, 2, and 7i as zeros.

Find the zeros of each polynomial function. a. f(x)=x3x22x b. f(x)=2x4+2x2

Given the following information about a polynomial function, find the function. It has a zero of multiplicity 3 at x=12 and another zero at x=3 . It contains the point (1,8).

Find the rational zeros of fx=2x3+x213x+6.

Graph the polynomial P(x)=(x+2)3+27, showing clearly all x- and y-intercepts.

Write the quadratic function in f(x)=a(xh)2+k form whose graph is shown.

Find the cubic polynomial function f with real coefficients that has 1 and 2+i as zeros, and f2=2.