Question

What is the degree of the polynomial and describe the end behavior of the graph – 5x² + x? - 11x + x + 1

A) Degree: 3; End behavior: As x approaches negative infinity, the graph goes down to the left. As x approaches positive infinity, the graph goes up to the right.
B) Degree: 4; End behavior: As x approaches negative infinity, the graph goes up to the left. As x approaches positive infinity, the graph goes up to the right.
C) Degree: 2; End behavior: As x approaches negative infinity, the graph goes up to the left. As x approaches positive infinity, the graph goes down to the right.
D) Degree: 1; End behavior: As x approaches negative infinity, the graph goes down to the left. As x approaches positive infinity, the graph goes down to the right.

Answer 1

The given polynomial is – 5x² ‑ 10x + 1 and it has a degree of 2. The end behavior, considering the leading coefficient is negative, will have the graph going up to the left as x approaches negative infinity and down to the right as x approaches positive infinity, which corresponds to option C.

Step-by-step explanation:

The polynomial in question is – 5x² + x ‑ 11x + x + 1. We can simplify this by combining like terms to get – 5x² ‑ 10x + 1. The degree of the polynomial is the highest power of x that appears in the polynomial, which in this case is 2 (from the term – 5x²). Therefore, the degree of the polynomial is 2.

Since the leading coefficient (the coefficient of the highest power term) is negative, the end behavior of the graph will be such that as x approaches negative infinity, the graph goes up to the left and as x approaches positive infinity, the graph goes down to the right. This matches the description of end behavior in option C. Hence, the correct answer is C) Degree: 2; End behavior: As x approaches negative infinity, the graph goes up to the left. As x approaches positive infinity, the graph goes down to the right.