Question

what should be subtracted from the polynomial x^4 + 2x^3 + x^2 - 18x - 15 so that the resulting polynomial is exactly divisible by x^2 - 1 - x.
HINT : SUBTRACT THE REMAINDER​

Answer 1

Answer:

$-10x^{2}$

Step-by-step explanation:

Aim is to make exactly divisible by $x^{2} - 1 - x$

$x^{4} + 2x^{3} + x^{2} - 18x - 15$

= $x^{4} - x^{3} - x^{2} + 3x^{3} -3x^{2} - 3x + 15x^{2} - 15x - 15 - 10x^{2}$

= $(x^{2} - 1 - x)$$(x^{2} + 3x + 15) - 10x^{2}$

$-10x^{2}$ need to be subtracted.