Can this polynomial be factored

Not solved, just factored? Can it be factored?
x^3 - 7x - 6
Thanks!

Yes is can!

(x+1)(x+2)(x-3)

Have a good day!

According to the Fundamental theorem of Algebra, f(x)=x^3-7x-6 has at least 1 real zero in the set of real numbers, call this zero a. By the factor theorem, (x-a) is a factor of f(x).
Trial and error yields f(-1)=0, f(2)=0, and f(3)=0
f(x)=(x+1)(x-2)(x-3)

yes. it helps to set the equation equal to zero in order to factor.

x^3 - 7x - 6 =0

by inspection, we can see that x=-1 satisfies this equation.

so factor out (x+1)

(x+1)*(x^2-x-6)

and x^2-x-6 also factors, giving you

(x+1) * (x+2) * (x-3)

Yes. Its Factors are (x+2) , (x+1), and (x-3)