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what does simple factors mean?

meaning (x+1) (x+2)(x+4) something like this

it can't be (2x+1), right?

simple had me too, i wanna say integers but simple can mean nothing in math :)

(x^3-7x)+(px^2-6)
x(x^2 - 7) + p(x^2 - 6/p)
p = 6/7 if i see it right

let us say p=0 the equation will be x^3-7x-6 = x^2(x+1)-x(x+1)-6(x+1)=(x-3)(x+2)(x+1).

but this is not concrete solution ..this is hit and trial...As choices were 0,1,2,3

try vieta formula

possible rational roots are pm 1, pm 2, pm 3, pm 6

0 is it according to the trial and error method :)

\[x^3+px^2-7x-6=x^x(x+p)-(7x+6)=(x^2-1)(x+p) =(x^2-1)(7x+6)\]
hence x+p=7x+6
p=6x+6

when p= 0 -> f(x) = x^3 - 7x - 6
= ( x + 1) ( x^2 - x - 6)
=> x = -1, x = -2, x = 3