What is the full equation of P(x)?

Question

Given P(x)= -x^3 + 3x^2 + x + 3. Write P in factored form (as a product of linear function). Be sure to include P(x)=

Answer 1

-x^3 +3x^2 + x + 3 doesn't have any integer factors

but

if maybe you got one sign wrong

so

P(x) = -x^3 +3x^2 -x +3

then

P(x) = -(x-3)(x^2 +1) and if you want imaginary factors

P(x) =-(x-3)(x-i)(x+i)

BUT if you stick with the original -x^2 +3x^2 +x +3 with the x term positive

the zero or root is between x=3 and x=4 and a factor between (x-3) and (x-4)

Answer 2

-x^3 +3x^2 + x + 3 doesn't have any integer factors

but

if maybe you got one sign wrong

so

P(x) = -x^3 +3x^2 -x +3

then

P(x) = -(x-3)(x^2 +1) and if you want imaginary factors

P(x) =-(x-3)(x-i)(x+i)

BUT if you stick with the original -x^2 +3x^2 +x +3 with the x term positive

the zero or root is between x=3 and x=4 and a factor between (x-3) and (x-4)