Question

factorise x³-23x²+142x-110
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Answer 1

QUESTION -

factorise x³-23x²+142x-110

ANSWER -

x3- 23x2+142x-120

let p(x)= x3- 23x2+142x-120

g(x)=x-1

0=x-1

x=1

p(1)=(1)3-23(1)2+142(1)-120

=1-23+142-120

=143-143

=0

Hence x-1 is a factor of x3- 23x2+142x-120

by long division

x3- 23x2+142x-120 = (x-1)(x2+22x+120)

=(x-1)(x2+10x+12x+120)

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

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