Answer the questions about the following polynomial.
minus, 7, plus, start fraction, x, cubed, divided by, 10, end fraction, minus, 5, x
−7+
10
x
3
−5x
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 two terms. The constant term is -7, the leading term is x^3/10, and the leading coefficient is 1/10.
To understand the polynomial, let's break it down step by step.
The polynomial expression is:
-7 + (x^3/10) - 5x
Step 1: Identify the constant term
The constant term is a term that does not contain any variable. In this polynomial, the constant term is -7.
Step 2: Identify the leading term
The leading term is the term with the highest degree. In this polynomial, the leading term is (x^3/10).
Step 3: Identify the leading coefficient
The leading coefficient is the coefficient of the leading term. In this polynomial, the leading coefficient is 1/10.
So, the polynomial has 3 terms. The constant term is -7, the leading term is (x^3/10), and the leading coefficient is 1/10.
To answer the questions about the given polynomial, let's first break down the expression and identify its parts:
The polynomial is: -7 + (x^3/10) - 5x
Now, let's go through each question step by step:
1. How many terms are in the polynomial?
To determine the number of terms, we need to count the individual parts that are separated by addition or subtraction signs. In this case, we have three terms:
Term 1: -7
Term 2: (x^3/10)
Term 3: -5x
Therefore, there are three terms in the polynomial.
2. What is the constant term?
The constant term is the term without any variables. In this polynomial, the constant term is -7.
3. What is the leading term?
The leading term is the term with the highest exponent on the variable. In this polynomial, the leading term is (x^3/10).
4. What is the leading coefficient?
The leading coefficient is the coefficient (number) multiplied by the leading term. In this polynomial, the leading coefficient is 1/10.
So, to summarize:
- The polynomial has 3 terms.
- The constant term is -7.
- The leading term is (x^3/10).
- The leading coefficient is 1/10.