Math, asked by raushanzamir2647, 9 months ago

: Factorise x3 – 23x2 + 142x - 120.

Answers

Answered by pulakmath007
11

SOLUTION

TO FACTORISE

 \sf{ {x}^{3}  - 23 {x}^{2} + 142x - 120 }

EVALUATION

 \sf{ {x}^{3}  - 23 {x}^{2} + 142x - 120 }

For x = 1 the above expression vanishes

So x - 1 is a factor of the expression

 \sf{ {x}^{3}  - 23 {x}^{2} + 142x - 120 }

 \sf{  = {x}^{3} -  {x}^{2}   - 22 {x}^{2} + 22x + 120x - 120 }

 \sf{  = {x}^{2}(x - 1)   - 22x( x - 1) + 120(x - 1) }

 \sf{  = (x - 1)({x}^{2}  - 22x+ 120) }

 \sf{  = (x - 1) \bigg[{x}^{2}  - 22x+ 120 \bigg]  }

 \sf{  = (x - 1) \bigg[{x}^{2}  -(12 + 10)x+ 120 \bigg]  }

 \sf{  = (x - 1) \bigg[{x}^{2}  -12x  -  10x+ 120 \bigg]  }

 \sf{  = (x - 1) \bigg[x(x - 12)  -  10(x -  12) \bigg]  }

 \sf{  = (x - 1) \bigg[(x - 12) (x -  10) \bigg]  }

 \sf{  = (x - 1) (x - 10) (x -  12)  }

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Answered by hareem23
2

Solution

TO FACTORISE

x³ - 23x² + 142x - 120

EVALUATION

x³ - 23x² + 142x - 120

For x = 1 the above expression vanishes

So x - 1 is a factor of the expression

x³ - 23x² + 142x - 120

= x³ - x² - 22 x² + 22x + 120x - 120

= x²(x - 1) - 22x( x - 1) + 120(x - 1)

= (x - 1)(x² - 22x+ 120)

=(x−1)[x² −22x+120]

=(x−1)[x² −(12+10)x+120]

=(x−1)[x² −12x−10x+120]

=(x−1)[x(x−12)−10(x−12)]

=(x−1)[(x−12)(x−10)]

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

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