Question

the remainder when the polynomial p(x) = x4-3x2+3x+1 is divided by x-1

Answer 1

Reminder is - 1
When we divide it the quotient is x3-x2+x+4

Answer 2

For zero, x - 1 = 0
=>x = 1

Let
$p(x) = {x}^{4} - 3 {x}^{2} + 3x + 1 \\ = > p(1) = {(1)}^{4} - 3 \times {(1)}^{2} + 3 \times 1 + 1 \\ \: \: \: \: \: \: \: \: \: = 1 - 3 + 3 + 1 \\ \: \: \: \: \: \: \: \: \: = 2$
Therefore, Remainder = 2