Question

find the remainder when x²+3x²+3x+1 is divided by x+1 by long division method photo answer will be helpful​

Answer 1

Correct Question :

Find the remainder when x³+3x²+3x+1 is divided by x+1 by long division method .

Answer :

0

Solution :

Please refer to the attachment .

Alternative 1

Using 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 p(x) = x³ + 3x² + 3x + 1 . We need to find the remainder when p(x) is divided by (x + 1) .

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

Thus ,

The remainder obtained when p(x) is divided by (x + 1) will be given as ;

=> R = p(-1)

=> R = (-1)³ + 3(-1)² + 3(-1) + 1

=> R = -1 + 3 - 3 + 1

=> R = 0

Hence , required remainder is 0 .

Alternative 2

By inspection :

• Factor theorem : If (x±c) is a factor of the polynomial p(x) , then the remainder obtained on dividing p(x) by (x±c) is 0 .

Let p(x) = x³ + 3x² + 3x + 1 . We need to find the remainder when p(x) is divided by (x + 1) .

Now ,

=> p(x) = x³ + 3x² + 3x + 1

=> p(x) = (x + 1)³

Clearly , (x + 1) if a factor of p(x) = (x + 1)³ .

Thus , the remainder obtained on dividing p(x) by (x + 1) will be 0 .

Hence , required remainder is 0 .

Answer 2

Answer:

Step-by-step explanation:

given :

find the remainder when x²+3x²+3x+1 is divided by x+1 by long division method

to find :

divided by x+1 by long division

solution :

• = x3 + 3x2 + 3x + 1

• (i) The root of x + 1 = 0 is -1

• p(-1) = (-1)3 + 3(-1)2 + 3(-1) + 1

• = -1 + 3 - 3 + 1

• = 0

• Hence by the remainder theorem, 0 is the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1.