Question

Which of the following is a linear polynomial-
A)p(x) = 58
B)p(x) = 65
C)p(x) = 43
D)p(x) = 58 + 65 +43 + x

Answer 1

Hint: There are many types of polynomials classified on the basis of their degree The degree of a polynomial is the highest power of the variable in that polynomial. For example, a polynomial with degree 2 is called a quadratic polynomial.

Complete step-by-step answer:

A linear polynomial is the one where the highest power if x is 1, that is, its degree is 1. In options A, B and C, we can clearly see that there is no variable and they are constant polynomials. Their degree is 0.

But in option D, we can see that there is a term x which has degree one, which means that it is a linear polynomial. The type of polynomial does not depend on the other terms, it only depends on the highest power of the variable.

Hence, the correct option is D. p(x) = 58 + 65 + 43 + x

Note: Students may get confused with the terms 58, 65 and 43 in option D. We should always keep in mind the fact that the degree of polynomial depends only on the highest power, no matter how many terms there are.