Question

what must be subtracted from 4x⁴-2x³-6x²+x-5,so that the results is exactly divisible by 2x²+x-1 ?​

Answer 1

Answer:

-write the dividend and divisor as 4x^4 - 2x^3 - 6x^2 + x -5 and

2x^2 + x - 2.

(4x^4 - 2x^3 - 6x^2 + x -5) divided by (2x^2 + x - 2) gives a quotient of 2x^2 - 2x and a remainder of -3x-5.

So you need to subtract (-3x-5) from the dividend.

Check: (4x^4 - 2x^3 - 6x^2 + x -5) -(-3x-5)

= 4x^4 - 2x^3 - 6x^2 + x -5 + 3x + 5

= (4x^4 - 2x^3 - 6x^2 + 4x) divided by (2x^2 + x - 2) gives a quotient of 2x^2 - 2x and a remainder of 0. Correct.

So you need to subtract (-3x-5) from the dividend.