Answer the questions about the following polynomial.
1, plus, one half, x, to the power 5 , minus, 2, x, squared
1+
2
1
x
5
−2x
2
Answer
Attempt 1 out of 2
The expression represents a
polynomial with
terms. The constant term is
, the leading term is
, and the leading coefficient is
.
The expression represents a polynomial with three terms. The constant term is 1, the leading term is x^5, and the leading coefficient is 1/2.
The polynomial expression given is 1 + (1/2)x^5 - 2x^2.
To analyze this polynomial, we can look at the terms individually:
1. The constant term is 1, which means there is no x variable present in this term. It is the term without any powers of x.
2. The leading term is (1/2)x^5. The leading term is the term with the highest power of x, which in this case is x^5.
3. The leading coefficient is (1/2). The leading coefficient is the coefficient of the leading term, which in this case is (1/2).
Therefore, the polynomial has 3 terms, with a constant term of 1, a leading term of (1/2)x^5, and a leading coefficient of (1/2).
To answer these questions about the given polynomial, let's break down the polynomial expression:
1/2x^5 - 2x^2
Question 1: How many terms are there in the polynomial?
To find the number of terms in a polynomial, count the number of plus or minus signs between the terms. In this case, there is only one plus sign, so the polynomial has 2 terms.
Answer: There are 2 terms in the polynomial.
Question 2: What is the constant term?
The constant term is the term that does not have any variable raised to a power. In this case, the constant term is "1."
Answer: The constant term is 1.
Question 3: What is the leading term?
The leading term is the term with the highest power of the variable. In this case, the leading term is "1/2x^5."
Answer: The leading term is 1/2x^5.
Question 4: What is the leading coefficient?
The leading coefficient is the coefficient of the leading term, which is the number in front of the variable with the highest power. In this case, the leading coefficient is "1/2."
Answer: The leading coefficient is 1/2.