Question

Degree of the polynomial $f\left(x\right)=\frac{(x^3+x^2-4)(x^3-8)}{(x-2)}$

• A. $5$
• B. $6$
• C. $9$
• D. $f\left(x\right)$ is not a polynomial

Answer 1

The correct option is A $5$

$f\left(x\right)=\frac{(x^3+x^2-4)(x^3-8)}{(x-2)}$

$=\frac{(x^3+x^2-4)(x-2)(x^2+2x+4)}{(x-2)}$

$=(x^3+x^2-4)(x^2+2x+4)$

$=x^5+2x^4+4x^3+x^4+2x^3+4x^2-4x^2-8x-16$

$=x^5+3x^4+6x^3-8x-16$

$\therefore$ Degree of $f\left(x\right)$ is $5$