Q. 23.7( 7 Votes )

# In each of the fo

Answer :

We have,

f(x) = 3x4+17x3+9x2-7x-10 and g(x) = x+5

In order to find whether the polynomials g (x) = x – (-5) is a factor of f (x) or not, it is sufficient to show that f (-5) = 0

Now,

f(x) = 3x4+17x3+9x2-7x-10

f (-5) = 3 (-5)4 + 17 (-5)3 + 9 (-5)2 – 7 (-5) – 10

= 3 * 625 + 17 * (-125) + 9 * 25 + 35 – 10

= 1875 – 2125 + 225 + 35 – 10

= 0

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

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