Question

Given 5 examples of linear polynomial, quadratic and cubic polynomial.

Answer 1

Hint: Each of the polynomials has a specific degree and based on that they have been assigned a specific name and are thus referred to as different types of polynomials. There are four types of polynomials – constant, linear, quadratic, and cubic polynomials. We have to give examples of each type of polynomial.

Complete step-by-step answer:
We know that,
Polynomials are classified on degree and here, the term degree means power. And this further determines the maximum number of solutions a function could have and the number of times a function will cross the x-axis when graphed.
A polynomial having degree zero is called Constant polynomial. In general $$f\left(x\right)=c$$ is a constant polynomial.

The types of polynomial are below:
1) Linear Polynomials:-
A linear polynomial is a polynomial of degree one, i.e., the highest exponent of the variable is one.
Here, we define an equation in the form:
$$p\left(x\right):ax+b,a\ne 0$$
Given below are a few examples of linear polynomials:
I.$$x+3$$
II.$$4x+{\displaystyle \frac{2}{5}}$$
III.$$-2x$$
OV.$$x+\sqrt{2}$$
V.$$\pi x+\sqrt{3}$$
We note that a linear polynomial in one variable can have at most two terms if ‘a’ is 0, then this will become a constant polynomial.

2) Quadratic Polynomials:-
A quadratic polynomial is a polynomial of degree two, i.e., the highest exponent of the variable is two. In general, a quadratic polynomial will be of the form:
$$p\left(x\right):a{x}^2+bx+c,a\ne 0$$
Given below are a few examples of quadratic polynomials:
I.$$2x^2+2x+1$$
II.$$x^2-4$$
III.$$\sqrt{2}{x}^2$$
IV.$$4x^2+{\displaystyle \frac{1}{7}}$$
V.$$2-x^2+x\surd 3$$
VI.$$x^2\surd 5+{\displaystyle \frac{2}{3}}x-6$$
We observe that a quadratic polynomial can have at most three terms and if ‘a’ is 0, then this will become a linear polynomial.

3) Cubic Polynomials:-
A cubic polynomial is a polynomial of degree three, i.e., the highest exponent of the variable is three. A cubic polynomial, in general, will be of the form:
$$p\left(x\right):a{x}^3+b{x}^2+cx+d,a\ne 0$$
Given below are a few examples of cubic polynomials:
I.$$2-x^3$$
II.$$\text{81}{x}^3-\text{ 5}$$
III.$$\pi x^3+{\left(\sqrt{2}\right)}^{11}$$
IV.$$x^3$$
V.$$3x^3-2x^2+x-1$$
VI.$$x^3\surd 2$$
We observe that a cubic polynomial can have at most four terms and if ‘a’ is 0, then this will become a quadratic rather than a cubic polynomial.

Note: After converting any expression into the general form, if the exponent of the variable in any term is not a whole number, then it's not a polynomial either. A polynomial of degree n will have n number of zeros or roots. A linear polynomial has only one zero. A quadratic polynomial can have at most two zeros, whereas a cubic polynomial can have at most 3 zeroes.