Answer:
The value to be added to the polynomial x³ - 6·x² + 11·x + 8 so that it is completely divisible by 1 - 3·x + x² is -(x + 11)
Step-by-step explanation:
By long division, we have;
= x - 3
-(x³ - 3·x² + x)
-3·x² + 10·x + 8
-(-3·x² + 9·x -3)
x + 11
Therefore, -(x + 11) should be added to the polynomial x³ - 6·x² + 11·x + 8 so that it is completely divisible by 1 - 3·x + x².
That is (x³ - 6·x² + 11·x + 8 - x - 11) ÷ (1 - 3·x + x²) = x - 3.