Question

When (x³ + 31) is divided by (x + 1), the remainder is​

Answer 1

Answer:

• Remainder is 30.

Solution:

Remainder theorem:

When a polynomial f (x)  is divided by $\sf{x-\alpha}$, then the remainder can be given by f ($\alpha$).

Comparing x + 1 and x-$\alpha$, we get

=> $\alpha$= -1

By Remainder theorem

f (x) = $\sf{x^{3}+31}$

Remainder = f (-1)

f (-1) = $\sf{(-1)^{3}+31}$

=> f (-1) = -1 + 31

=> f (-1) = 30

Hence, the remainder is 30.

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Extra information:

• By remainder theorem we can say that when $\sf{x^{n}+y^{n}}$ is divided by (x + y) then the remainder is $\sf{(-y)^{n}+y^{n}}$

Answer 2

When a polynomial f (x)  is divided by , then the remainder can be given by f ().

Comparing x + 1 and x-, we get

=> = -1

By Remainder theorem

f (x) =

Remainder = f (-1)

f (-1) =

=> f (-1) = -1 + 31

=> f (-1) = 30

Hence, the remainder is 30.