Question

The degree of the polynomial $f\left(x\right)=\left|\begin{array}{ccc}1& 4& 20\\ 1& -2& 5\\ 1& 2x& 5x^2\end{array}\right|$ is

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

By using sarrus rule:
$\begin{array}{ccccc}1& 4& 20& 1& 4\\ 1& -2& 5& 1& -2\\ 1& 2x& 5x^2& 1& 2x\end{array}$
$=-10x^2+20+40x-20x^2-10x+40\Rightarrow f\left(x\right)=-30x^2+30x+60$
$\therefore$Degree of $f\left(x\right)$ is $2$