Question

factories : x³ + 13x² + 32x + 20​

Answer 1

Answer:

take X common and ther will be

Step-by-step explanation:

x^2+13x+32+20

then do it

Answer 2

AnswEr-:

• $\underline{\boxed {\mathrm {\blue{ Factors \:are\:-:(x+1)(x + 10) ( x + 2)} }}}$

Explanation-:

• Factorise -: x³ + 13x² + 32x + 20 .

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

• $\longrightarrow {\mathrm { x^{3}+ 13x^{2} + 32x + 20 }}$

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

• $\sf{In\:Second \:Term\:-:}$

• $\longrightarrow {\mathrm { x^{3} + \purple{13x^{2}} + 32x + 20 }}$

• $\longrightarrow {\mathrm { x^{3} + \purple {x^{2} + 12x^{2}} +40x + 20 }}$

• $\sf{In\:Third \:Term\:-:}$

• $\longrightarrow {\mathrm { x^{3} + x^{2} + 12x^{2} + \purple{32x} + 20 }}$

• $\longrightarrow {\mathrm { x^{3} + x^{2} + 12x^{2} +\purple {12x+20x} + 20 }}$

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

• $\longrightarrow {\mathrm { x^{3} + x^{2} + 12x^{2}+ 12x + 20x + 20 }}$

$\sf{ By\:Taking\:x^{2}\:as \:common\:in\:First \:term-:}$

• $\longrightarrow {\mathrm { \purple {x^{3} + x^{2}} + 12x^{2}+ 12x + 20x + 20 }}$

• $\longrightarrow {\mathrm { \purple {x^{2} (x + 1)} + 12x^{2}+ 12x + 20x + 20 }}$

$\sf{ By\:Taking\:12x\:as \:common\:in\:Second \:term-:}$

• $\longrightarrow {\mathrm { x^{2} (x + 1) + \purple {12x^{2}+ 12x} + 20x + 25 }}$

• $\longrightarrow {\mathrm { x^{2} (x + 1) + \purple {12x(x+ 1)} + 20x + 25 }}$

$\sf{ By\:Taking\:20\:as \:common\:in\:Second \:term-:}$

• $\longrightarrow {\mathrm { x^{2} (x + 1) + 12x(x+ 1) + \purple{20x + 20} }}$

• $\longrightarrow {\mathrm { x^{2} (x + 1) + 12x(x+ 1) + \purple{20(x + 1) }}}$

$\sf{ By\:Taking\:(x+1)\:as \:common\:in\:expression-:}$

• $\longrightarrow {\mathrm { x^{2} \purple{(x + 1)} + 12x\purple{(x+ 1)} +20 \purple{(x + 1)} }}$

• $\longrightarrow {\mathrm { (x+1 ) \purple{(x^{2} + 12x + 20)}}}$

$\sf{\dag{ By\:Using \:Sum-\:Product \:pattern\:in\:formed\:expression-:}}$

• $\longrightarrow {\mathrm { (x+1 ) \purple{ ( x^{2} + 12x + 20)} }}$

• $\longrightarrow {\mathrm { (x+1 ) \purple {( ( x^{2} + 10x+2x + 20)} }}$

$\sf{ Now\:Finding \:Common-\:Factors \:from\:new\:formed\:expression-:}$

• $\longrightarrow {\mathrm { (x+1 ) \[ ( x^{2} + 10x+2x + 20)\] }}$

• $\sf{ By\:Taking\:x\:as \:common\:in\:first \:term\:in\:formed\:expression-:}$

• $\longrightarrow {\mathrm { (x+1 ) \[ ( \purple{x^{2} + 10x}+2x + 20)\] }}$

• $\longrightarrow {\mathrm { (x+1 ) \[ ( \purple{x(x+10 )}+2x + 20)\] }}$

• $\sf{ By\:Taking\:2\:as \:common\:in\:second\:term\:in\:formed\:expression-:}$

• $\longrightarrow {\mathrm { (x+1 ) \[ ( x(x+10 )+\purple {2x + 20})\] }}$

• $\longrightarrow {\mathrm { (x+1 ) \[ x(x+10 )+\purple {2(x + 10)})\] }}$

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

• $\longrightarrow {\mathrm {\purple{(x+1 ) \[ x(x+10 )+\purple {2(x + 10)})\]} }}$

• $\longrightarrow {\mathrm { \purple{(x+1)(x+10)(x+2)} }}$

Hence ,

• $\underline{\boxed {\mathrm {\blue{ Factors \:are\:-:(x+1)(x + 10) ( x + 2)} }}}$

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