Question #6453339Fill in the Blank
Algebra-1
Question
Consider the polynomial . As , the value of approaches __________.
Answer & Analysis
Analysis
Question Analysis
This question evaluates the student's understanding of the end behavior of a polynomial function with an even degree and a positive leading coefficient.
This question evaluates the student's understanding of the end behavior of a polynomial function with an even degree and a positive leading coefficient.
Key Concept Explanation
The end behavior of a polynomial is determined by the leading term, which is the term with the highest degree. The sign of the leading coefficient and the parity (even or odd) of the degree dictate the end behavior.
The end behavior of a polynomial is determined by the leading term, which is the term with the highest degree. The sign of the leading coefficient and the parity (even or odd) of the degree dictate the end behavior.
Step-by-step Solution
1. Identify the leading term: The leading term is , with a leading coefficient of 5 and an even degree of 8.
2. Determine the end behavior for negative infinity: Since the leading coefficient is positive and the degree is even, as
1. Identify the leading term: The leading term is , with a leading coefficient of 5 and an even degree of 8.
2. Determine the end behavior for negative infinity: Since the leading coefficient is positive and the degree is even, as
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