Which of the following describes the end behavior of the polynomial P(x) = -2x^4

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Question: Which of the following describes the end behavior of the polynomial P(x) = -2x^4 + 3x^3 - x + 5?

Options:

Correct Answer: Both ends go down.

Solution:

Since the leading coefficient is negative and the degree is even, both ends of the polynomial go down.

Which of the following describes the end behavior of the polynomial P(x) = -2x^4 + 3x^3 - x + 5?

Which of the following describes the end behavior of the polynomial P(x) = -2x^4 + 3x^3 - x + 5?

Step 1: Identify the polynomial given, which is P(x) = -2x^4 + 3x^3 - x + 5.
Step 2: Find the degree of the polynomial. The degree is the highest exponent of x, which is 4 in this case.
Step 3: Determine the leading coefficient. The leading coefficient is the number in front of the term with the highest degree, which is -2.
Step 4: Analyze the degree. Since the degree (4) is even, we know that both ends of the polynomial will behave the same way.
Step 5: Analyze the leading coefficient. Since the leading coefficient (-2) is negative, this means that both ends of the polynomial will go down.
Step 6: Combine the information from steps 4 and 5 to conclude that both ends of the polynomial go down.

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