# The polynomial of degree 4, P(x) has a root multiplicity 2 at x=4 and roots multiplicity 1 at x=0 and x=-4 and it goes through the point (5, 18) how do you find a formula for p(x)?

The polynomial is

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To find a formula for ( P(x) ), we utilize the fact that when a polynomial has a root of multiplicity ( m ) at ( x = a ), its factorization includes ( (x - a)^m ). Given the information provided, the factorization of ( P(x) ) would be ( (x - 4)^2 \cdot x \cdot (x + 4) ). To determine the coefficient of ( P(x) ), we use the given point ( (5, 18) ) by substituting ( x = 5 ) into the polynomial equation and solving for the coefficient. With this information, we can write the formula for ( P(x) ).

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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.

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.

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.

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