How do you create a polynomial p which has zeros #c=+-2, c=-1#, and the leading term is #117x^4#?

Answer 1

#117*(x-2)(x+2)(x+1)^2#

That is one of many. To find this, remember that to say that a polynomial has a zero at c is to say that P is proportional to (x-c)^n where n is the multiplicity of the root.

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Answer 2

Serenity Jones

To create a polynomial (p) with zeros (c = \pm 2), (c = -1), and a leading term of (117x^4), you can use the zero-product property. The factors corresponding to the zeros are ((x - 2)), ((x + 2)), and ((x + 1)).

To get the leading term to be (117x^4), you can introduce a constant multiplier. So, the polynomial (p) would be (117(x - 2)(x + 2)(x + 1)(x + 1)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.