Question

Examine whether (x+2) is a factor of ( x*x*x + 3*x*x + 5*x + 6)

Answer 1

For convenience, name the polynomial P(x).

Now, (x+2) should be a factor of P(x).

We can show it as : P(x)=(x+2)Q(x)+R

Check whether the polynomial doesn't have remainder.

We should find x which makes (x+2)Q(x) equal 0.

x +2 = 0, x = -2 is the solution.

Now substitute the value of x.

P(-2) =R

P(-2) = (-8) +12 -10 +6 = 0 ∴ R = 0

Therefore, there is no remainder. x+2 is a factor of P(x).