Question

If $x^{140}+2x^{151}$ + k is divisible by x + 1, then the value of k is

• A. 1
• B. -3
• C. 2
• D. -2

Answer 1

The correct option is A

1

$\therefore$ x + 1 is a factor of f(x) = $x^{140}+2x^{151}$ + k

$\therefore$ Remainder will be zero

Let x + 1 = 0, then x =-1

$\therefore$ f(-1) $=(-1{)}^{140}+2(-1{)}^{151}$ + k

= 1 -2+ k=k-1

{$\because$ 140 is even and 151 is odd}

$\because$ Remainder = 0

$\therefore$ k-1= 0 $\Rightarrow$ k=1