Using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the by actual division
Question:
Using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the by actual division
$f(x)=9 x^{3}-3 x^{2}+x-5, g(x)=x-2 / 3$
Solution:
Here, $f(x)=9 x^{3}-3 x^{2}+x-5$
g(x) = x − 2/3
from, the remainder theorem when f(x) is divided by g(x) = x - 2/3 the remainder will be equal to f(2/3)
substitute the value of x in f(x)
$f(2 / 3)=9(2 / 3)-3(2 / 3)^{2}+(2 / 3)-5$
= 9(8/27) − 3(4/9) + 2/3 − 5
= (8/3) − (4/3) + 2/3 − 5
$=\frac{8-4+2-15}{3}$
$=\frac{10-19}{3}$
= - 9/3
= - 3
Therefore, the remainder is - 3