Question

factories the given Q

Answer 1

x^3 - 23x^2 + 142x - 120

=> x^3 - x^2 - 22x^2 + 22x + 120x - 120

=> x^2 ( x - 1) - 22x ( x - 1) + 120(x - 1)

=> ( x - 1) (x^2 - 22x +120)

=> ( x - 1) (x^2 - 12x - 10x +120)

=> (x - 1)[ x(x - 12) - 10(x - 12)]

=> (x - 1)(x - 12)(x - 10)

Answer 2

Hello , dear
......★________here, is Ur answer ..
Hope u will understand ....

Qus.is factories x² - 23x² + 142x - 120

Let p(x) = x² - 23x² + 142x - 120

checking p(x) = 0
_____________________________

x = x ³ - 23x² + 142x - 120
0= 0³ - 23 (0)² + 142 (0) - 120
=> -120
whether 0 is Not

so , we check with 1
X= x³ - 23x² + 142x - 120
1 = 1³ - 23 (1)² + 142 (1 ) - 120
1 = 1 - 23 + 142 - 120
=> 143 - 143
=> 0
si , at x = 1 , p(x) =0
______________________________
we checked .
hence , x-1 is a factor of p (x)

Now, p(x ) = (x - 1 ) g(x )

=>g(x ) = p(x)/(x -1)

=> g(x) is obtained after dividing p(x) by x - 1
if we divided by x - 1 , we have x² - 22x + 120

so, g (x ) = x² - 22x + 120

so, p (x ) = ( x - 1 ) g (x )
=> (x - 1 ) ( x² - 22x + 120 )
we factorize g (x) i.e. x² - 22x + 120

we factorize using the splitting the middle term method

X² - 22x + 120

=> x² - 12x - 10x + 120

=> x (x - 12) - 10 ( x - 12 )

=> ( x - 12 ) ( x - 10 )

so , p( x ) = ( x - 1 ) ( x - 10 ) ( x - 12 )

ANSWER IS ( x – 1 ) ( x – 10 ) ( x – 12 )

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