Question

what must be subtracted from (x4+2x³-2x²+4x+6) so that the result is exactly divisible by( x² +2x-3)?​

Answer 1

hello mate,

$( {x}^{4} + {2x}^{3} - {2x}^{2} + 4x + 6) - (y) = {x}^{2} + 2x - 3 \\ \\ \\ - y = ({x}^{2} + 2x - 3) - ( {x}^{4} + \\ {2x}^{3} - {2x}^{2} + 4x + 6) \\ \\ \\ - y = {x}^{2} + 2x - 3 - \\ {x}^{4} - {2x}^{3} + {2x}^{2} - 4x + 6 \\ \\ \\ - y = - {x}^{4} - {2x}^{3} + {3x}^{2} - 2x + 3 \\ \\ y = {x}^{4} +\\ {2x}^{3} - {3x}^{2} + 2x - 3$

soo,

${ x}^{4} + {2x}^{3} - {3x}^{2} + 2x - 3$

should be subtracted from (x4+2x³-2x²+4x+6) to get ( x² +2x-3)

hope it will help you