Math CentralQuandaries & Queries


Question from john, a student:

here is a word problem that my teacher gave us to do can you help me understand it

Give possible formulas (in factored form) and sketch the graphs for two different polynomials that have roots -3, -1, and 2, but cross the x-axis only at x=2 and have y-intercept 4.5. What is the lowest degree such a polynomial can have? Can it have an even degree? An odd degree? Explain why.

her term "root" has completely thrown me off, i've reviewed my book and cant find what she is referring to. can anyone help?

Hi John,

If p(x) is a polynomial then a root of p(x) is a number a such that p(a) = 0. Your book might call it a zero of the polynomial.

Is this enough to get you started? If you need further assistance write back.


John wrote back

i'm afraid that i'm still not completely understanding
i now understand that the -3, -1, and 2 are the zero's of the functions, but i dont see how to use them to find the formulas for two functions if you could demonstrate where to "plug them in" along with what is done with the x and y intercepts that are given, it should be enough to get me started. is this possible for you to do?
thank you


The next step is the factor theorem which says that if a is a root of a polynomial p(x) then (x - a) is a factor of the polynomial. Thus if a is a root of p(x) then p(x) = (x - a)q(x) for some polynomial q(x).


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