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

F(x) = x

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)(x

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}

F(x) = x

^{3}+4x^{2}+x -6We 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)(x

^{2}+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}