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Let $a x^{3}+b x^{2}+c x+d=\left|\begin{array}{lcc}x+1 & 2 x & 3 x \\ 2 x+3 & x+1 & x \\ 2-x & 3 x+4 & 5 x-1\end{array}\right|$ then
What is the value of $\mathrm{c}$ ?
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What is the value of $\mathrm{c}$ ?
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Verified Answer
The correct answer is:
35
$a x^{3}+b x^{2}+c x+d$
$=(x+1)[(x+1)(5 x-1)-x(3 x+4)]-2 x[(2 x+3)(5 x-1)$
$-x(2-x)]+3 x[(2 x+3)(3 x+4)-(2-x)(x+1)]$
$\Rightarrow a x^{3}+b x^{2}+c x+d=x^{3}+28 x^{2}+35 x-1$
$\Rightarrow c=35$
$=(x+1)[(x+1)(5 x-1)-x(3 x+4)]-2 x[(2 x+3)(5 x-1)$
$-x(2-x)]+3 x[(2 x+3)(3 x+4)-(2-x)(x+1)]$
$\Rightarrow a x^{3}+b x^{2}+c x+d=x^{3}+28 x^{2}+35 x-1$
$\Rightarrow c=35$
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