What is the zeros, degree and end behavior of #y=-2x(x-1)(x+5)#?
Zeroes
Degree Polynomial of third degree End behaviour
Zeroes
This is very easy: the function is already written in its factorized form. So, if you want to solve
you are asking for a multiplication to be zero. A multiplication is zero if and only if at least one of its factors is zero, so the alternatives are
Degree
Just by eyeballing the equation, you can tell this is a polynomial of degree three, since it's the multiplication of three degrees of degree one.
But just to be sure, let's do the actual multiplications:
End Behaviour
Since you have a minus sign in front of the polynomial, the limits will be inverted.
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To find the zeros, degree, and end behavior of the polynomial function (y = -2x(x-1)(x+5)), first, set the function equal to zero and solve for (x):
(-2x(x-1)(x+5) = 0)
The zeros of the function occur when each factor equals zero:
- (x = 0) (from (x))
- (x = 1) (from (x - 1))
- (x = -5) (from (x + 5))
So, the zeros of the function are (x = 0), (x = 1), and (x = -5).
The degree of the polynomial function is determined by the highest power of (x) in the expression, which is 3.
The end behavior of the function can be determined by looking at the leading term of the polynomial. In this case, the leading term is (x^3). As (x) approaches positive infinity ((+\infty)), the leading term (x^3) dominates the function, so the end behavior is as follows:
- As (x) approaches positive infinity ((+\infty)), (y) approaches positive infinity ((+\infty)).
- As (x) approaches negative infinity ((-\infty)), (y) approaches negative infinity ((-\infty)).
Therefore, the zeros of the function are (x = 0), (x = 1), and (x = -5), the degree is 3, and the end behavior is as described.
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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.
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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