Question

উৎপাদকে বিশ্লেষণ কর: $(x-1)(x-3)(x-5)(x-7)$$-65$

Answer 1

$=(x-1)(x-3)(x-5)(x-7)$$-65$

$=(x-1)(x-7)(x-3)(x-5)$$-65$

$=\left\lbrace x(x-7)-1(x-7)\right\rbrace$$\left\lbrace x(x-5)-3(x-5)\right\rbrace-65$

$=\left(x^2-7x-x+7\right)$$\left(x^2-5x-3x+15\right)-65$

$=\left(x^2-8x+7\right)$$\left(x^2-8x+15\right)-65$

$=\left(x^2-8x+7\right)$$\left(\underline{x^2-8x+7}+8\right)-65$

ধরি,
$x^2-8x+7=p$

তাহলে প্রদত্ত রাশি দাঁড়ায়,
$p\left(p+8\right)-65$

$=p^2+8p-65$

$=p^2+13p-5a-65$

$=p\left(p+13\right)-5\left(a+13\right)$

$=\left(p+13\right)\left(p-5\right)$

$=\left(x^2-8x+7+13\right)$$\left(x^2-8x+7-5\right)$
[ মান বসিয়ে ]

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