Question

Classify the following as linear, quadratic and cubic polynomials:
(a)${{x}^{2}}+x$
(b)$x-{{x}^{3}}$
(c)$y+{{y}^{2}}+4$
(d)1+x
(e)3t
(f)${{r}^{2}}$
(g)$7{{x}^{3}}$

Answer 1

Hint: We will first state the definition of degree and how it is related to linear, quadratic and cubic polynomials. And then we will use the definition to classify all the given options as linear or quadratic or cubic.

Complete step-by-step answer:
Let’s first write the definition of terms:
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.
Now we will write the meaning of linear, quadratic and cubic.
Linear: The degree of polynomial is 1.
Quadratic: The degree of polynomial is 2.
Cubic: The degree of polynomial is 3.
Now we will check each of the options and find out in which category from the above three they belong.
For (a): ${{x}^{2}}+x$
It’s degree is 2, hence it is quadratic.
For (b): $x-{{x}^{3}}$
It’s degree is 3, hence it is cubic.
For (c): $y+{{y}^{2}}+4$
It’s degree is 2, hence it is quadratic.
For (d): 1 + x
It’s degree is 1, hence it is linear.
For (e): 3t
It’s degree is 1, hence it is linear.
For (f): ${{r}^{2}}$
It’s degree is 2, hence it is quadratic.
For (g): $7{{x}^{3}}$
It’s degree is 3, hence it is cubic.

Note: Here one should be aware of the term degree and using this we have given the definition of linear, quadratic and cubic. So, to distinguish between these three one should understand the definition completely.