Question

Find the remainder when x 3-a x 2+6 x -a is divided by x -a​

Answer 1

Answer :-

Given that x³ - ax² + 6x - a is divided by ( x - a ) .

So , by Remainder Theorem , when any polynomial say p(x) is divided by ( x - a ) , then remainder is p(a) .

Step 1 : Equate the divisor with 0 .

=> x - a = 0.

=> x = 0 + a.

=> x = a

Step 2 : Put x = a in p(x) .

=> p(x) = x³ - ax² + 6x - a

=> p(a) = a³ - a³ + 6a - a

=> p(a) = 5a .

Hence remainder is 5a.