Question

find the remainder when 9x3-3x2+x-5 is divided by (x-2/3)

Answer 1

By Remainder Theorem,

$x = \frac{2}{3}$


Hence,


$=> 9 {( \frac{2}{3}) }^{3} - 3 {( \frac{2}{3} )}^{2} + \frac{2}{3} + 5 = r \\ \\ \\ => 9( \frac{8}{27} ) - 3(\frac{4}{9} ) + \frac{2}{3} - 5 = r \\ \\ \\ => \frac{8}{3} - \frac{4}{3} + \frac{2}{3} - 5 = r \\ \\ \\ => \frac{8 - 4 + 2 - 15}{3} = r \\ \\ \\ => - \frac{9}{3} = r \\ \\ \\ => - 3 = r$



Hence, remainder is –3

Answer 2

Here is your answer

x = 2/3

put x = 2/3 in 9x³-3x²+x-5

9*(2/3)³ - 3*(2/3)² + 2/3-5
9*8/27 - 3* 4/9 + 2/3 -5
8/3 - 4/3 + 2/3 - 5
8-4+2-15/3
-9/3
-3

Hope it helps you ^_^