Question

find the remainder when the polynomial px = xcube -5 xsqure+ x- 5 is duvided by 1-3 x​

Answer 1

Answer:

Hello dear user

Here is your answer

$given \: p(x) = {x}^{3} - 5 {x}^{2} + x - 5 \\ g(x) = 1 - 3x \\ we \: have \: to \: divide \: p(x) \: by \: g(x) \\ \: g(x) = 1 - 3x \\1 - 3x = 0 \\ 1 = 3x \\ x = \frac{1}{3} \\ now \: putting \: value \: of \: x = \frac{1}{3} \: in \: p(x) \\ p(x) = {x}^{3} - 5 {x}^{2} + x - 5 \\ p( \frac{1}{3}) = ( \frac{1}{3})^{3} - 5( { \frac{1}{3} })^{2} + \frac{1}{3} - 5 \\ p(\frac{1}{3}) = \frac{1}{27} - \frac{5}{9} + \frac{1}{3} - 5 \\ p(\frac{1}{3}) = \frac{1 - 15 + 9 - 135}{27} \\ p(\frac{1}{3}) = \frac{ - 140}{27} \\ so \: remaimder \: is \: ( \frac{ - 140}{27})$

Hope it is clear to you.