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 .

Given :

• A polynomial x³+3x²+3x+1 is divided by x+1 .

To Find :

• Remainder .

Solution :

$\longmapsto\tt{x+1=0}$

$\longmapsto\tt{x=-1}$

$\longmapsto\tt\bf{{x}^{3}+{x}^{2}+3x+1}$

Putting x = -1 :

$\longmapsto\tt{{(-1)}^{3}+{(-1)}^{2}+3x+1}$

$\longmapsto\tt{=-1+3-3+1}$

$\longmapsto\tt\bf{0}$

So , The Remainder is 0 .

Answer 2

Answer:

Appropriate Question :-

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

Given :-

• A polynomial x³ + 3x² + 3x + 1 is divided by x + 1.

To Find :-

• What is the remainder.

Solution :-

$\mapsto$ x³ + 3x² + 3x + 1 is divided by x + 1.

✭ At first :

$\leadsto \bf x + 1$

By putting divisor = 0 we get,

$\leadsto \sf x + 1 =\: 0$

$\leadsto \sf x =\: 0 - 1$

$\leadsto \sf x =\: - 1$

$\leadsto \sf\bold{\purple{x =\: - 1}}$

✭ Now :

$\implies \bf x^3 + 3x^2 + 3x + 1$

By putting x = - 1 we get,

$\implies \sf (- 1)^3 + 3(- 1)^2 + 3(- 1) + 1$

$\implies \sf (- 1)(- 1)(- 1) + 3(- 1)(- 1) + (- 3) + 1$

$\implies \sf (1)(- 1) + 3(1) - 3 + 1$

$\implies \sf - 1 + 3 - 3 + 1$

$\implies \sf 2 - 3 + 1$

$\implies \sf - 1 + 1$

$\implies \sf\boxed{\bold{\red{0}}}$

$\therefore$ The remainder is 0 .

[Note :- Please refer the attachment for the long division method. ]