Question

17 Which one of the following statements is correct
(a) if x6 + 1 is divided by x + 1, then the remainder is –2.
(b) if x6 + 1 is divided by x – 1, then the remainder is 2.
(c) if x6 + 1 is divided by x + 1, then the remainder is 1.
(d) if x6 + 1 is divided by x – 1, then the remainder is –1.

Answer 1

Answer:

When divided by x + 1

$f(x) = {x}^{6} + 1$

$x + 1 = 0 \\ x = - 1$

So remainder will be

$f( - 1) = ( - 1) {}^{6} + 1 = 2$

Similarly when divide by x - 1

or

$x - 1 = 0 \: or \: x = 1$

Remainder will be

$f(1) = (1) {}^{6} + 1 = 2$

So answer is

Option 2

Answer 2

$\huge\bigstar\underline\mathcal\purple{Answer:-}$

Option b) is your correct answer

Hope it helps!!✔✔