Question

Find the factors of -:x^2 + 18 x + 81

No Spam Allowed :​

Answer 1

AnswEr-:

• $\underline{\boxed {\mathrm {\red{ Factors \:are\:-:(x + 9) ( x + 9)} }}}$

Explanation-:

• Find factors of -: x² + 18x + 81 .

$\dag{\mathrm { Solution \:of\: Question-:}}$

• $\longrightarrow {\mathrm { x^{2} + 18x + 81 }}$

$\sf{ By\:Using \:Sum-\:Product \:pattern-:}$

• $\longrightarrow {\mathrm { x^{2} + \purple{18x} + 81 }}$

• $\longrightarrow {\mathrm { x^{2} + \purple {9x + 9x} + 81 }}$

$\sf{ Now\:Finding \:Common-\:Factors \:from\:each\:term-:}$

• $\longrightarrow {\mathrm { x^{2} + 9x + 9x + 81 }}$

$\sf{ By\:Taking\:x\:as \:common\:in\:First \:term-:}$

• $\longrightarrow {\mathrm { \purple {x^{2} + 9x} + 9x + 81 }}$

• $\longrightarrow {\mathrm { \purple {x(x + 9)} + 9 x + 81 }}$

$\sf{ By\:Taking\:9\:as \:common\:in\:Second \:term-:}$

• $\longrightarrow {\mathrm { x(x + 9) + \purple{ 9 x + 81} }}$

• $\longrightarrow {\mathrm { x(x + 9) + \purple{ 9 ( x + 9)} }}$

$\sf{ Now,\:Rewrite \:the\:factored\:term\:\:-:}$

• $\longrightarrow {\mathrm { x(x + 9) + 9 ( x + 9) }}$

• $\longrightarrow {\mathrm { \purple{(x + 9) ( x + 9)} }}$

Hence ,

• $\underline{\boxed {\mathrm {\blue{ Factors \:are\:-:(x + 9) ( x + 9)} }}}$

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Answer 2

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀☆ GIVEN⠀ POLYNOMIAL  – x² + 18x  + 81 :

⠀⠀⠀⠀

$:\implies\sf x^2 +18x + 81 = 0 \\\\\\\star \sf{By \:Using\:Sum-Product \:Pattern\::}\\\\ \:\implies\sf x^2 + 9x + 9x + 81= 0 \\\\\\\star\sf{Finding\:out\:Common\:Terms\::}\\\\\\:\implies\sf x(x + 9) +9(x + 9) = 0\\\\\\\star\sf{Now,\:Rewrite\:in\:Factored\:term\::}\\\\\\:\implies\sf (x + 9)\; (x + 9) = 0\\\\\\:\implies{\underline{\boxed{\frak{\purple{(x+9)(x+9)}}}}}\;\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence, \:The\:factors\:are\:\bf{(x+9)\:and \:(x+9)\: }}}}$

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