Question

Which one of the following statement is correct? (1) If x^6 + 1 is divided by x + 1 reminder is -2. (2) If x^6 + 1 is divided by x - 1 reminder is 2. (3) If x^6 + 1 is divided by x + 1 reminder is 1. (4) If x^6 + 1 is divided by x - 1 reminder is -1.

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Answer 1

$\maltese$ $\bold{\red{\underline{SOLUTION : }}}$ $\maltese$

$\rule{200}3$

•To understand the true statement each condition has to be considered

Let us consider the case (1)

When f(x) = $x^6$ + 1 is divided by x + 1 then the remainder is -2

Here x = -1 then

f(-1) = $(-1)^6$+ 1

f(-1) = 2

A statement (1) is wrong.

$\rule{200}3$

•Let us consider the case (2)

When f(x) = $x^6$+ 1 is divided by x – 1 then the remainder is 2

Here x = +1 then

f(1) = $(1)^6$+ 1

f(1) = 2

A statement (2) is correct.

$\rule{200}3$

•Let us consider the case (3)

When f(x) = $x^6$ + 1 is divided by x + 1 then the remainder is 1

Here x = -1 then

f(-1) =$(-1)^6$+ 1

f(1) = -2

A statement (3) is wrong.

$\rule{200}3$

•Let us consider the case (4)

When f(x) = $x^6$ + 1 is divided by x – 1 then the remainder is -1

Here x = +1 then

f(-1) = $(1)^6$ + 1

f(1) = 2

A statement (4) is wrong.

$\rule{200}3$