If x2+5x+1x+1x+2x+3=ax+1+bx+1x+2+cx+1x+2x+3and A=abc1then det A is

x2+5x+1=ax+2x+3+bx+3+ca=1; 5a+b=5; 6a+3b+c=1 b=0 c=−5A=10−51⇒det A=1

If x2+5x+1x+1x+2x+3=ax+1+bx+1x+2+cx+1x+2x+3and A=abc1then det A is

x2+5x+1=ax+2x+3+bx+3+ca=1; 5a+b=5; 6a+3b+c=1 b=0 c=−5A=10−51⇒det A=1

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If $\frac{x^{2} + 5 x + 1}{(x + 1) (x + 2) (x + 3)} = \frac{a}{x + 1} + \frac{b}{(x + 1) (x + 2)} + \frac{c}{(x + 1) (x + 2) (x + 3)}$ and $A = [\begin{matrix} a & b \\ c & 1 \end{matrix}]$ then det A is

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$x^{2} + 5 x + 1 = a (x + 2) (x + 3) + b (x + 3) + c$
$a = 1; 5 a + b = 5; 6 a + 3 b + c = 1$
$b = 0 c = - 5$
$A = [\begin{matrix} 1 & 0 \\ - 5 & 1 \end{matrix}] \Rightarrow \det A = 1$

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If x2+5x+1x+1x+2x+3=ax+1+bx+1x+2+cx+1x+2x+3and A=abc1then det A is

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If $\frac{x^{2} + 5 x + 1}{(x + 1) (x + 2) (x + 3)} = \frac{a}{x + 1} + \frac{b}{(x + 1) (x + 2)} + \frac{c}{(x + 1) (x + 2) (x + 3)}$ and $A = [\begin{matrix} a & b \\ c & 1 \end{matrix}]$ then det A is