Question

what must be subtracted from the polynomial 4x4+2x3 -8x2 +3x-7so that it must be exactly divisible by2x2+x-2

Answer 1

Thus 5x - 11 should be subtracted so that it can be exactly divisible by 2x² +x - 2
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Answer 2

Lets divide (4x4 - 2x3 - 6x2 + x - 5) by (2x2 + x – 1) as shown.



Hence (−6) should be subtracted from (4x4 − 2x3 − 6x2 + x − 5) so that the resulting polynomial is exactly divisible by (2x2 + x – 1).