Question

find the reminder when 3x*4- x*3+1 is divisible by (x-1)​

Answer 1

❏Appropriate Question:-

• Find the reminder when, $3 {x}^{4} - {x}^{3} + 1$ is divisible by (x-1)

❏Solution:-

$\pink{x - 1 = 0} \\ \\ \\ \color{magenta} \boxed {x = 1}$

Let,

$\\ \color{pink}p(x) = {3x}^{4} - {x}^{3} + 1$

Putting x = 1

$\\ \green{p(1) = {3(1)}^{4} - (1) {}^{3} + 1 }\\ \\ \\ \\ \color{teal} = 3(1) - 1 + 1 \\ \\ \\ \\ \color{green} \underline \color{green}{\fbox{= 3}}$

Hence, The remainder is 3 after dividing $3 {x}^{4} - {x}^{3} + 1 \:$ by $(x - 1).$