Question

Which of the following is a linear polynomial? Write the correct alternative answer for each of the following questions.
A. \[x + 5\]
B. \[{x^2} + 5\]
C. \[{x^3} + 5\]
D. \[{x^4} + 5\]

Answer 1

Hint: Here in this question, we have to find out the linear polynomial along given four polynomials. To find this check the degree of each polynomial then the polynomial having degree 1 is a linear polynomial or monomial, polynomial having 2 degree is quadratic polynomial or binomial, degree 3 is cubic polynomial or trinomial and degree 4 is bi-quadratic polynomial.

Complete step-by-step answer:
Polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division.
The highest power of the variable in a polynomial is called the degree of the polynomial.
Based on the degree we can tell find out the linear polynomial easily:
Consider the given question
A. \[x + 5\]
It is a one variable polynomial, variable having a degree one then it is called as linear polynomial.
B. \[{x^2} + 5\]
Variable having a degree two, then it is a quadratic polynomial.
C. \[{x^3} + 5\]
Variable having a degree three, then it is a cubic polynomial.
D. \[{x^4} + 5\]
Variable having a degree four, then it is a Bi-quadratic polynomial.
Hence, \[x + 5\] is only a linear polynomial.

So, the correct answer is “Option A”.


Note: The classification of one variable polynomial based on degree, let us first understand the meaning of the degree of a polynomial.
The highest power of the variable in a polynomial is called the degree of the polynomial.
For a multivariable polynomial, it is the highest sum of powers of different variables in any of the terms in the expression.
Based on the degree of a polynomial in one variable, it can be classified as:
A polynomial having 0 as the degree of the polynomial is termed as zero or constant polynomial.
A polynomial with 1 as the degree of the polynomial is termed as linear polynomial or monomial.
A polynomial of degree 2, i.e., the highest exponent of the variable is 2 termed as quadratic polynomial or binomial.
A polynomial of degree 3, i.e., the highest exponent of the variable is 3 termed as cubic polynomial or trinomial.