Algebra II; Analyzing graphs of polynomials
- Thread starter divliar
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We cannot, within this environment, replace the missing classroom lectures or the chapter in the textbook. To learn about this topic, please study online lessons, such as this one.
After you have studied the entire lesson (or others you've found online), please attempt the exercise. If you get stuck, please reply with your thoughts regarding the minimum degree of the five-turning-point polynomial, your thoughts on the minimum degree of the three-zeroes polynomial, and your thoughts regarding the leading degree of their product polynomial.
When you reply, please include the assignment's specifications, if any, regarding the type of zeroes for the second polynomial. In particular, must these zeroes be real (so they're also x-intercepts), or may they be complex? Thank you!
Okay, so you have three polynomials in this problem. Let's call the first one f(x), the second g(x), and the third h(x). What do you know from reading the problem?
f(x) has 5 turning points
g(x) has 3 zeros
h(x) = f(x) * g(x)
Given that f(x) has 5 turning points, what is its degree? Can you say exactly what degree it is? If not, can you perhaps say the maximum or minimum degree it can be? Similarly, given that g(x) has 3 zeros, what is its degree? And finally, given that h(x) is the other two polynomials multiplied together, what is its degree?
f(x) has 5 turning points
g(x) has 3 zeros
h(x) = f(x) * g(x)
Given that f(x) has 5 turning points, what is its degree? Can you say exactly what degree it is? If not, can you perhaps say the maximum or minimum degree it can be? Similarly, given that g(x) has 3 zeros, what is its degree? And finally, given that h(x) is the other two polynomials multiplied together, what is its degree?