Using Factor Theorem To Factorise Completely F(x)=x^3+4x^2+x-6 Hence Solving Equation X^3+4x^2+x-6=0,Can You Help Me?

The factor theorem tells us that if F(k)=0, (x-k) is a factor of the polynomial.

F(x) = x³ +4x² +x -6

We can see that the sum of the coefficients is 0, so we know F(1)=0, and x-1 is a factor.
F(x) = (x-1)(x² +5x +6)

Because all of the coefficients of the quadratic are positive, we know that roots of that will all be negative. Let's try x=-2
F(-2) = (-2-1)(4 -10 +6) = 0

So,
F(x) = (x-1)(x+2)(x+3)

The solution to F(x)=0 is x = {-3, -2, 1}