Question

What must be subtracted from x⁴ + 6x³ + 13x² + 13x + 8 so that the resulting polynomial is exactly divisible by (x² + 3x + 2).​

Answer 1

Answer:

$x4 + 6x3 + 13x2 + 13x + 8 -( y) = x2 + 3x + 2 \\ - (y) = x2 + 3x + 2 - (x4 + 6x3 + 13x2 + 13x + 8) \\ - y = - x4 - 6x3 - 12x2 - 10x - 6 \\y = x4 + 6x3 + 12x2 + 10x + 6 \\ answer \: is \: x4 + 6x3 + 12x2 +10x + 6$