Answer the questions about the following polynomial.
one seventh, x, to the power 5 , minus, 3, plus, 9, x
7
1
x
5
−3+9x
Answer
Attempt 1 out of 2
The expression represents a blank
polynomial with
terms. The constant term is
, the leading term is
, and the leading coefficient is
.
The expression represents a polynomial with 3 terms. The constant term is -3, the leading term is x^5, and the leading coefficient is 1/7.
The expression represents a polynomial with 3 terms. The constant term is -3, the leading term is x^5, and the leading coefficient is 1.
To determine the number of terms in the polynomial, count the number of separate expressions (or summands) that are added or subtracted. In this case, there are three separate expressions: 1/7, x^5, and -3+9x. Therefore, the polynomial has 3 terms.
To identify the constant term, look for the term without any variable. In this case, the constant term is -3.
To determine the leading term, find the term with the highest exponent of x. Here, the highest exponent is 5, so the leading term is x^5.
The leading coefficient of a polynomial is the coefficient of the leading term. In this case, the leading coefficient is 1/7.
Therefore, the polynomial is a 3-term polynomial with a constant term of -3, a leading term of x^5, and a leading coefficient of 1/7.