Question

Choose the correct answer from the alternatives given :
The reminder when ($k{x}^2$ + x + 1) is divided by (x + 2k) is

• A. -2k - 1
• B. k - 1
• C. $4k^3$ + 2k - 1
• D. $4k^3$ - 2k + 1

Answer 1

The correct option is D $4k^3$ - 2k + 1

$(x+2k)\sqrt{{kx}^2+x+1}kx+(1-{2k}^2)$

$\underset{–}{{kx}^2+2k^{2}x}$

$x(1-{2k}^2)+1$

$\underset{–}{x(1-{2k}^2)+2k(1-2k^2)}$

$\underset{–}{1-2k+4k^3}$

So, remainder is ${4k}^3-2k+1$