Question

using remanider thorem find the remainder when x3 +x2+x -1 is divide d by x-1​

Answer 1

Answer:

$let \: p(x) = {a}^{3} + {ax}^{2} + 2x - a$

$g(x) = x - a$

$=> x - a = 0$

$=> x = a$

The reminder when p(x) is divided by g( x) is p(3)

The reminder when p(x) is divided by g( x) is p(3)....( By reminder theorem)

$Thus \: p(a) = {a}^{3} - a {(a)}^{2} + 2(a)$

$\: \: \: \: \ \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: = {a}^{3} - {a}^{3} + 2a - a \: \\ therefore \: \\ reminder = a$

Answer 2

Answer:

$let \: p(x) = {a}^{3} + {ax}^{2} + 2x - a$

$g(x) = x - a$

$=> x - a = 0$

$=> x = a$

The reminder when p(x) is divided by g( x) is p(3)

The reminder when p(x) is divided by g( x) is p(3)....( By reminder theorem)

$Thus \: p(a) = {a}^{3} - a {(a)}^{2} + 2(a)$

$\: \: \: \: \ \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: = {a}^{3} - {a}^{3} + 2a - a \: \\ therefore \: \\ reminder = a$