Question

show that (x-2),(x+3)and (x-4) are the factors of x3-3x2-10x+24​

Answer 1

Answer:

x^3-3x^2-10x+24

=x^3-2x^2-x^2+2x-12x+24

=x^2(x-2)-x(x-2)-12(x-2)

=(x-2)(x^2-x-12)

=(x-2)(x^2-4x+3x-12)

=(x-2){x(x-4)+3(x-4)}

=(x-2) (x-4) (x+3)

so , (x-2) , (x-4) , (x+3) are the factors of

x^3-3x^2-10x+24