Problem
Two examples of each of the following:
i) Give an example of a polynomial of degree 7 in nonfactored form.
ii) Now give an example of a polynomial of degree 7 in factored form that has exactly 3 zeros. Label it f(x).
iii) For each of the zeros of f(x) tell whether the graph crosses or touches the axis. How can you tell just by looking at the equation, whether the graph will touch or cross the axis at each particular zero.
iv) Now give an example of a polynomial of degree 7 in factored form. Label it L(x). Create L(x) such that L(5) = 0.
v) Create a polynomial of degree 6 in nonfactored form. Label it R(x). Create R(x) such that R(x) is greater than or equal to 0 for all values of x.
For part (i), the degree of a polynomial (when there's one variable) simply means the highest value of the exponent. So if we have a polynomial in one variable x, degree 7 could be something like this.
The response must include a reference list. Using Times New Roman 12 pnt font, double-space, one-inch margins, and APA style of writing and citations.