Question

is x+3 a factor of x^3+3x^2+2x+3

Answer 1

Let p(x) = x+3 and f(x) = x³ + 3x² + 2x + 3
We need to find out whether p(x) is a factor of f(x).

put p(x) = 0
⇒ x+3 = 0
⇒ x = -3

f(x) = x³ + 3x² + 2x + 3
⇒ f(-3) = (-3)³ + 3(-3)² + 2(-3) + 3
⇒ f(-3) = -27 + 27 - 6 + 3
⇒ f(-3) = -3  (remainder)

Since remainder is not 0, x+3 is not a factor of  x³ + 3x² + 2x + 3.

Answer 2

P(X) = X^3+3X^2+2X+3

I.E X+3 = 0
       X = -3

P(X) = (-3)^3+3(-3)^2+2(-3)+3
       = -27+3(9)-6+3
       =-27+27-6+3
       = -3
3+3 IS NOT A FACTOR OF P(X)