Question

Fill in the blanks:
A polynomial of degree 1 is called a _________________ polynomial.

Answer 1

Hint: A polynomial is an expression that is made up of variables and coefficients, involving the different mathematical operations –addition, subtraction, multiplication, division. Degree of a polynomial is the highest power to which the variable or variables are raised in a polynomial.

Complete step-by-step answer:
A polynomial, can sometimes contain only one variable with different powers or have different variables with different powers, involving the different mathematical operations. For example, $4{x^2} - 2x + 1$ is a polynomial is one variable.
On the other hand $2{x^2} - {y^2} = 5$ is a polynomial in two variables.
Now, we can also classify polynomials on the basis of the highest power of the variable or variables in the polynomial, whether there is just one or more than one variables.
A polynomial which has a variable or variables whose highest power is 1, that is their degree is 1, is called a linear polynomial. Now let us understand this in two ways:
First Case- One variable whose highest power is 1.
For example, let us consider the polynomials$4x + 5 = 0$ and, $2y - 3 = 0$. Now in both these polynomials, there is only one variable- x and y respectively and the highest power to which they have been raised is 1. Hence both these polynomials are of degree 1. Therefore, these are linear polynomials or linear equations.
Second Case-More than one variable, highest power is 1
Now, let us consider the polynomials $2x + 3y - 9 = 0$ , $3a + 5b + 3c + 1 = 0$ , $ - 2x + 3y - 7z = 4$ . In all of these three polynomials, what we can clearly observe is the variables are more than one in the equation but the highest power to which the variables are raised is 1. Therefore the degree of these polynomials is 1. Hence all these polynomials are linear equations in two variable or linear equations in more than two variables.
Hence, we conclude that when a polynomial, whether it contains one variable or more than one variable, if the highest power to which the variables are raised is 1, that is their degree is 1, then the polynomial is called a linear polynomial.
So, we will use the word Linear to fill the blank on the right side.
So the sentence will now become:
A polynomial of degree 1 is called a linear polynomial.

Note: The classification of polynomials as per the degree other than 1 are:
A polynomial of degree 2 is called a quadratic polynomial while a polynomial of degree 3 is called a cubic polynomial. A polynomial of degree 4 is called a bi-quadratic polynomial.
Another classification of polynomial is done on the basis of the number of terms as:
A polynomial with just one term is called a monomial. A polynomial with two terms is called a binomial.