Question

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

Answer 1

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).