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For the following polynomial, determine the degree, leading term and the end behavior for y = -x⁵-5x³-3x² 7x+1

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Final answer:

The given polynomial has a degree of 5, a leading term of -x⁵, and its end behavior is such that y approaches negative infinity as x approaches positive infinity and y approaches positive infinity as x approaches negative infinity.

Step-by-step explanation:

The degree of the polynomial y = -x⁵-5x³-3x²+7x+1 is determined by the highest power of x in the equation, which in this case is 5. Therefore, the degree of the polynomial is 5. The leading term of the polynomial is the term with the highest power of x, which is -x⁵. To determine the end behavior of the polynomial, we look at the leading term. Since the coefficient of the leading term is negative and the degree is odd, as x approaches positive infinity, y will approach negative infinity, and as x approaches negative infinity, y will approach positive infinity.

User Aman Aggarwal
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