Question

p(x) = x5+3x4-x3-3x+5x+15 divided by x+3​

Answer 1

If g(x) is a factor of f(x), then the remainder will be zero that is g(x) = 0.  g(x) = x + 3 = 0, then x = -3

Remainder = f(-3)

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

= -243 + 3 x 81 -(-27)-3 x 9 + 5(-3) + 15

= -243 + 243 + 27 - 27 - 15 + 15  = 0

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

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