Question

5.
Find the remainder when x - x? +x+6 is divided by x + 1
A) 3
(B) 9
(C-3
(D) 1​

Answer 1

Question :

Find the remainder when x³ - x² + x + 6 is divided by (x + 1) .

Answer :

(A). 3

Method 1 :

By actual division

x + 1 ) x³ - x² + x + 6 ( x² - 2x + 3

x³ + x²

– –

– 2x² + x

– 2x² - 2x

+ +

3x + 6

3x + 3

– –

3

Clearly ,

Remainder , R= 3

Method 2 :

By Remainder theorem

★ Remainder theorem : If a polynomial p(x) is divided by (x - c) , then the remainder obtained is given as R = p(c) .

Let the given polynomial be p(x) .

Thus ,

p(x) = x³ - x² + x + 6

If x + 1 = 0 , then x = -1 .

Thus ,

If p(x) is divided by x + 1 , then the remainder will be given as p(-1) .

Thus ,

=> R = p(-1)

=> R = (-1)³ - (-1)² + (-1) + 6

=> R = -1 - 1 - 1 + 6

=> R = 3

Hence ,

Remainder , R = 3