The constant term of the polynomial left|begi | vedclass

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(C) Let $f(x) = \left|\begin{array}{ccc} x+3 & x & x+2 \ x & x+1 & x-1 \ x+2 & 2x & 3x+1 \end{array}ight|$.To find the constant term,we can set $x

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$-1$

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(C) Let $f(x) = \left|\begin{array}{ccc} x+3 & x & x+2 \ x & x+1 & x-1 \ x+2 & 2x & 3x+1 \end{array}ight|$.To find the constant term,we can set $x = 0$ in the determinant.Substituting $x = 0$ into the determinant:$f(0) = \left|\begin{array}{ccc} 0+3 & 0 & 0+2 \ 0 & 0+1 & 0-1 \ 0+2 & 2(0) & 3(0)+1 \end{array}ight|$$f(0) = \left|\begin{array}{ccc} 3 & 0 & 2 \ 0 & 1 & -1 \ 2 & 0 & 1 \end{array}ight|$Expanding along the second column $(C_2)$:$f(0) = 0 - 1 	imes \left|\begin{array}{cc} 3 & 2 \ 2 & 1 \end{array}ight| + 0$$f(0) = -1 	imes (3(1) - 2(2))$$f(0) = -1 	imes (3 - 4)$$f(0) = -1 	imes (-1) = 1$Wait,let us re-evaluate the expansion of the polynomial $f(x) = 8x^2 + 9x - 1$. The constant term is the value of the polynomial when $x=0$. Evaluating $f(0) = 8(0)^2 + 9(0) - 1 = -1$. The previous expansion was correct,and the constant term is $-1$.

The constant term of the polynomial $\left|\begin{array}{ccc}x+3 & x & x+2 \\ x & x+1 & x-1 \\ x+2 & 2x & 3x+1\end{array}\right|$ is

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