precal question

Question

A polynomial P is given.

P(x) = x³ + x² + 4x

(a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

x=

(b) Factor P completely.

p(x)=

Answer 1

To solve this you need to set the function equal to 0 and then factor

x^3 +x^2 +4x =0

x(x^2 +x + 4)=0 so x= 0 and (x^+x +4) =0

x^2 +x+4 does not factor further so can use quadratic formula or completing the square to solve. I will use quadratic formula [-1 +/- sqroot (1-(4)(1)(4)] /2= [-1+sqroot(-15)] 2 and ‘-1-[sqroot-15]/2

so solutions are x=0, [-1+sqroot-15]/2, [-1-sqroot-15]/2