Question

${x}^{2}+ 32x -273$
Splitting This Equation​

Answer 1

$\sf\purple{\underline{\underline{Question}}}$

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$\small\tt{x^{2}\:+\:32x\:-273}$

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$\sf\purple{\underline{\underline{Answer}}}$

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$\small\tt{x^{2}\:+\:32x\:-273}$

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$\small\text{Splitting the middle term so there product }\\{\small\text{will be 273 and sum will be 32}}$

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$\small\text{Taking lcm of 273}$

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$\small\text{Factors we get , 3 , 13 , 7 }$

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$\small\text{Now taking these three factore in such way so}\\{\small\text{while adding we will get the sum of 32}}$

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$\small\tt{Will\:take\: (13\times3 - 7 \:= \:39\: -\: 7\: =\: 32)}$

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$\small\longrightarrow\tt{x^{2}\:+\:39x\:-7x\:-273}$

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$\small\longrightarrow\text{x (x+39) -7 (x+39)}$

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$\small\longrightarrow\text{(x-7) (x+39)}$

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$\small\longrightarrow\text{(x-7) (x+39) = 0}$

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$\small\longrightarrow\text{x-7 = 0 = 7}$

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$\small\longrightarrow\text{x+39 = 0 = -39}$

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$\small\text{We get the value of x are 7 and -39}$

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$\sf\purple{\underline{\underline{Thanks}}}$

Answer 2

$\dashrightarrow \sf \red{ {x}^{2} + 32x - 273} \\ \dashrightarrow \sf{ {x}^{2} + 39x - 7x - 273 } \\ \dashrightarrow\sf{x(x + 39) - 7(x + 39)} \\ \dashrightarrow\sf \red{(x - 7)(x + 39)}$