Chapter 1.1, Problem 122E

To determine

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

Answer to Problem 122E

No,the expression $\sqrt{x^2+7x+6}$ is not a polynomial.

Explanation of Solution

Given: It is given in the question that the expression is $\frac{x^2+3x+4}{x^2-9}$ .

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 $\sqrt{x^2+7x+6}$ .

Since ,A polynomial cannot be under a radical symbol.

The expression can be rewritten as ${(x^2+7x+6)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

Since , it is not a polynomial because it cannot have exponent ${}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ .

Conclusion:

No , it is not a polynomial.