Question

For $\frac{x^3+2x+1}{5}-\frac{7}{2}{x}^2-x^6$, write
i) the degree of the polynomial
ii) the coefficient of $x^3$
iii) the coefficient of $x^6$
iv) the constant term

Answer 1

The given polynomial is,

$\frac{x^3+2x+1}{5}-\frac{7}{2}{x}^2-x^6$

$=\frac{1}{5}{x}^3+\frac{2}{5}x+\frac{1}{5}-\frac{7}{2}{x}^2-x^6$

(1) Degree of the polynomial is the Highest degree of its terms, which is $6$ in this case (degree of $x^6$ )

(2) Coefficient of $x^3$ is $\frac{1}{5}$

(3) Coefficient of $x^6$ is $-1$

(4) The constant term in the polynomial is $\frac{1}{5}$