Question

factorise xcube-23xsquare+142x-120​

Answer 1

✯✯ QUESTION ✯✯

Factorise x³-23x²+142x-120..

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✰✰ ANSWER ✰✰

$\longmapsto\tt{Constant\:Term=120}$

➮Factors of Constant Term :-

1,2,3,4,5,6,8,10,12...

➥Now ,

$\longmapsto\tt{{x}^{3}-{23x}^{2}+142x-120}$

✒Putting p(x) = 1 : -

$\longmapsto\tt{{(1)}^{3}-23{(1)}^{2}+142(1)-120}$

$\longmapsto\tt{1-23+142-120}$

$\longmapsto\tt{-143+143}$

$\longmapsto\tt\bold{0}$

• x+1 is root of p (x)
• x-1 is a factor of p(x)

⠀⠀⠀⠀(Refer to the attachment)⠀⠀

➥Now ,

$\longmapsto\tt\bold{{x}^{2}-22x+120}$

By Splitting Middle Term : -

$\longmapsto\tt{{x}^{2}-(12x+10x)+120}$

$\longmapsto\tt{{x}^{2}-12x-10x+120}$

$\longmapsto\tt{x(x-12)-10(x-12)}$

$\longmapsto\tt\bold{(x-10)(x-12)}$

☛So , Three factors are (x-1) , (x-10) , (x-12)...

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