Question

factorise : x3 -23x2 +142x -120

Answer 1

Answer:(x-1)(x-10)(x-12)

Step-by-step explanation:

let p(x)=X^3-23x^2+142x-120

now we have to take p(x)=p(1)

(1)^3-23(1)^2+142(1)-120

1-23+142-120

143-143=0

here,x-1 is a factor of p(x)

f(x)=p(x)/(x-1)

x-1)x^3-23x^2+142x-120(x^2-22x+120

     x^3-X^

    (-)   (+)                                

          -22x^2+142x-120

          -22x^2+22x

          (+)        (-)                      

                       120x-120

                       120x-120

                      (-)      (+)                

                           0

so, f(x)=x^2-22x+120

so,

 p(x)=(x-1)f(x)

       = (x-1)(x^2-22x+120)

 

we factorized x^2-22x+120

=x^2-22x+120

=x^2-12x-10x+120

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

=(x-10)(x-12)

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