# In each of the fo

We have,

f(x) = x5+3x4-x3-3x2+5x+15 and g(x) = x+3

In order to find whether g (x) = x – (-3) is a factor of f (x) or not, it is sufficient to prove that f (-3) = 0

Now,

f(x) = x5+3x4-x3-3x2+5x+15

f (-3) = (-3)5 + 3 (-3)4 – (-3)3 – 3 (-3)2 + 5 (-3) + 15

= - 243 + 243 – (-27) – 3 (9) + 5 (-3) + 15

= - 243 + 243 + 27 – 27 – 15 + 15

= 0

Hence, g (x) is a factor of f (x).

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