The Factor Theorem

Question

Use the Factor Theorem to determine whether x + 3 is a factor of P(x) = x³ + 4x² - 9.Specifically, evaluate P at the proper value, and then determine whether x + 3 is a factor.

Is x+3 a factor of P(x) or not

P(?) = ?

Answer 1

x^3 + 4x^2-9

is x+3 a factor?

(-3)^3+ 4(-3)^2 -9= -27+36-9 =0

P(-3) = 0

yes, it's a factor of P(x),

the remainder is zero, when you do long or synthetic division

(x^3+4x^2-9)/(x+3) = x^2 + x -3

(x^2+x-3)(x+3) = exactly x^3+4x-9 with zero remainder

x=-3 or -1/2 + or -(1/2)sqr(1+12)

x=-3, .5+.5sqr13