Question

Classify the following as linear, quadratic and cubic polynomial: $ 5{x^2} + x - 7 $

Answer 1

Hint: Here, we are asked to classify the given polynomial as linear, quadratic or cubic. This classification can be determined by the degree of polynomial. The degree of polynomial is nothing but the highest value of exponent in the expression which is also known as the order of polynomials. Therefore, here we need to find the order of the given polynomial to determine whether it is linear, quadratic or cubic.

Complete step-by-step answer:
We are asked to classify the polynomial $ 5{x^2} + x - 7 $ . For this, our first step will be to see the power of variables in each term of the polynomial.
We can rewrite the polynomial as $ 5{x^2} + {x^1} - 7{x^0} $ .
From this, it is clearly seen that the power of variables in the first, second and third term is 2, 1 and 0 respectively.
Thus, the highest power or exponent in the polynomial is 2 and hence the degree of polynomial or the order of polynomial is 2.
Now, we know that,
If the degree or the order of the polynomial is 1, it is called linear polynomial.
If the degree or the order of the polynomial is 2, it is called quadratic polynomial.
If the degree or the order of the polynomial is 3, it is called cubic polynomial.
Here, we have seen that the degree of the given polynomial $ 5{x^2} + x - 7 $ is 2 and hence it is classified as the quadratic polynomial.
So, the correct answer is “Quadratic polynomial”.

Note: In this type of questions, it is important to keep in mind that when we are finding the degree of the polynomial, it should be arranged in ascending order, in which the degree of each term is at least as large as the degree of the preceding term, or in descending order, in which the degree of each term is no larger than the degree of the preceding term.. In the given polynomial $ 5{x^2} + x - 7 $ , the powers of the variable are already arranged in descending order.