Question

what must be subtracted from (x^4+2x³-2x+4x+6) so that the result is exactly divisible by (x²+2x-3)

Answer 1

$\textbf{ Hello Mate! }$

Let the remainder be in form of ax + b

On factoring $x^2 + 2x - 3$ we get,

${x}^{2} + 2x - 3 \\ {x}^{2} +3x - x - 3 \\ x(x + 3) - 1(x + 3)$
$\textbf{ \red{=> ( x - 1 )( x + 3 ) }}$

So, value of x = 1, - 3

Now, please go through once attatcment.

$\boxed{ \textsf{ Hence,\:a=1\:and\:b=-6 }}$

Have great future ahead!