Question

What must be subtracted from 4x4-2x3-6x2+x-5 so that the result is exactly divisible by 2x2+x-2

Answer 1

Answer:

- 4x⁴ + 2x³ + 8x² + 3

Step-by-step explanation:

Let the number be 'A'

(4x⁴ - 2x³ - 6x² + x - 5) - A = 2x² + x - 2

⇒ A =  2x² + x - 2 - (4x⁴ - 2x³ - 6x² + x - 5)

⇒ A =  2x² + x - 2 - 4x⁴ + 2x³ + 6x² - x + 5

⇒ A =  - 4x⁴ + 2x³ + 8x² + 3

So, (- 4x⁴ + 2x³ + 8x² + 3) must be subtracted from (4x⁴ - 2x³ - 6x² + x - 5)  to get  (2x² + x - 2)