Answer the questions about the following polynomial.
minus, 8, x, cubed, minus, 1
−8x
3
−1
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 cubic polynomial with four terms. The constant term is -1, the leading term is -8x^3, and the leading coefficient is -8.
-1. To write the polynomial in standard form, we arrange the terms in descending order of the exponents.
The polynomial can be written as:
-8x^3 - 1
To answer the questions about the polynomial, let's break down the given expression:
minus, 8, x, cubed, minus, 1
This can be written as:
-8x^3 - 1
Now let's answer the questions:
1. How many terms are there in the polynomial?
To find the number of terms in the polynomial, count the number of separate expressions separated by addition or subtraction signs. In this case, we have two separate expressions, -8x^3 and -1. Therefore, the polynomial has two terms.
2. What is the constant term?
The constant term is the term in the polynomial that does not contain any variables or variables with exponents. In this case, the constant term is -1.
3. What is the leading term?
The leading term is the term in the polynomial with the highest exponent. In this case, the leading term is -8x^3.
4. What is the leading coefficient?
The leading coefficient is the coefficient of the leading term, i.e., the number multiplied by the variable with the highest exponent. In this case, the leading coefficient is -8.
So, the answers to the questions are as follows:
- The polynomial has 2 terms.
- The constant term is -1.
- The leading term is -8x^3.
- The leading coefficient is -8.