Question

find the remainder when x³-3x²+3x-2 is divided by x+1​

Answer 1

Answer :-

Remainder = -9

Step-by-step explanation :-

Given:

• Dividend → f(x) = x³ - 3x² + 3x - 2
• Divisor → g(x) = (x + 1)

To find:

Remainder = ?

Solution:

For solving this question, apply remainder theorem. In this theorem equate g(x) to zero and then you will get a value of x. Substitute this value of x in f(x). Then, you will easily get the remainder without actual division.

   g(x) = 0

⇒ (x + 1) = 0

⇒ x + 1 = 0

⇒ x = -1

Substitute this value of x in f(x) to find the value of remainder.

f(x) = x³ - 3x² + 3x - 2

   f(-1) = (-1)³ - 3(-1)² + 3(-1) - 2

⇒ f(-1) = -1 - 3(1) - 3 - 2

⇒ f(-1) = -1 - 3 - 3 - 2

⇒ f(-1) = -9

∴ The remainder when (x³ - 3x² + 3x - 2) is divided by (x + 1) would be -9

Answer 2

EXPLANATION:-

Dividend- f(x)= x³ - 3x² + 3x - 2

Divisor- g(x)= (x + 1)

Let's apply the remainder theorem here which says that:-

Equate g(x) (divisor) with 0 and then whatever we get the value of x ,put the value in f(x) (dividend).Then we will get the remainder.

So let's equate g(x) with 0, we get:-

==>(x+1)=0

==>x=-1

So let's put the value in f(x), we get:-

==>f(x)= x³ - 3x² + 3x - 2

==>f(1)=(-1)³ - 3(-1)² + 3(-1)- 2

==>f(1)=-1-3-3-2

==>f(1)=-9

So the remainder is -9