Chapter 1.1, Problem 120E

To determine

Find wether the expression is a polynomial or not,if it is ,write the polynomial in standard form.

Answer to Problem 120E

Yes,the expression $2x^2-2x^4-x^3+\sqrt{2}$ is a polynomial.

Explanation of Solution

Given: It is given in the question that the expression is $2x^2-2x^4-x^3+\sqrt{2}$ .

Concept Used:

In this,use the concept of polynomial and also degree of polynomial as Linear polynomial(having degree $1$ ),Quadratic Polynomial (havind degree $2$ ),Cubic Polynomial (having degree $3$ ),Biquadratic polynomial (having degree $4$ ).

Calculation:

Here,the expression is $2x^2-2x^4-x^3+\sqrt{2}$ .

It has to be rearrange from the highest degree to the lowest degree.

  $\begin{array}{l}2x^2-2x^4-x^3+\sqrt{2}\\ \Rightarrow -2x^4-x^3+2x^2+\sqrt{2}\end{array}$

Since ,it has a degree 4 ,so it is a biquadratic polynomial and also it is a quadrinomial expression.

Conclusion:

Yes , it is a polynomial.