Question

What minimum must be added to 2 x cube minus 3 X square + 6 X + 7 to the resulting polynomial will be divisible by x square - 4 x + 8

Answer 1

The minimum value that must be added to 2x³ - 3x² + 6x + 7 so that the resulting polynomial is completely divisible by x² - 4x + 8 is -(2x+3).

We must add the remainder when 2x³ - 3x² + 6x + 7 is divided by x² - 4x + 8 to 2x³ - 3x² + 6x + 7 to make it completely divisible.

After solving using long division method , Remainder = -(2x+3)

So -(2x+3) must be added to the polynomial to make the resultant polynomial completely divisible by x² - 4x + 8.