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Question
f(x) = 3x4 + 17x3 + 9x2 − 7x − 10; g(x) = x + 5
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Solution
It is given that f(x) = 3x4 + 17x3 + 9x2 − 7x − 10 and g(x) = x - 5
By the factor theorem, g(x) is a factor of polynomial f(x)
i.e. x+5 =0
⇒ x= -5
Therefore,
\[f( - 5) = 3 \left( - 5 \right)^4 + 17 \left( - 5 \right)^3 + 9 \left( - 5 \right)^2 - 7\left( - 5 \right) - 10\]
\[ = 3 \times 625 + 17 \times \left( - 125 \right) + 225 + 35 - 10\]
\[ = 1875 - 2125 + 250\]
\[ = 0\]
Hence, g(x) is the factor of polynomial f(x).
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