Question

What type of polynomial is 3x-1. How many terms, The constant term, The leading term and the leading coefficient.

Answer 1

Polynomials in one variable are algebraic expressions that consist of terms in the form ax^(n) where n is a non-negative (i.e. positive or zero) integer and a is a real number and is called the coefficient of the term.

For √(3x-1)= (3x-1)^1/2

By converting the root to exponent form we see that there is a rational root in the algebraic expression. All the exponents in the algebraic expression must be non-negative integers in order for the algebraic expression to be a polynomial. As a general rule of thumb if an algebraic expression has a radical in it then it isn’t a polynomial.

Answer 2

Polynomials are mathematical expressions that have variables with different degrees and coefficients added together.

Terms

A term is part of a polynomial that is added to other terms. For example, take the polynomial 2x³ + 4x² - 7x + 3. This polynomial has 4 terms: 2x³, 4x², -7x, and 3. Each term is separated by addition.

The polynomial above, 3x-1, has 2 terms: 3x and -1. Polynomials that have 2 terms are known as binomials.

Constant Term

A constant is a number that does not change. Specifically, for polynomials, constants are terms that do not have variables. Since there is no variable, the number cannot change.

For our polynomial, the constant is -1. Since -1 has no variables, it is always constant.

Leading Term and Standard Form

The leading term is the first term when the polynomial is written in standard form. Standard form is when variables are written in order of degree. The degree is the exponent of the variable. For example, let's look at the non-standard form polynomial: 5x² - 4x³ + 4 - 7x. To put this polynomial in standard form, list the terms in decreasing degrees. So, start with x³ and end with the constant term (which has a degree of 0 because there is no variable).

• -4x³ + 5x² - 7x - 4

Now, the polynomial is in standard form. For this polynomial, the leading term is -4x³.

The polynomial we were given in the question is already in standard form. So, the leading term is just the first term, 3x.

Leading Coefficient

The leading coefficient is simply the coefficient of the leading term. Remember that a coefficient is the number that comes before the variable. Since the leading term is 3x, the leading coefficient is 3.