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Naya [18.7K]
3 years ago
5

What should be added in the polynomial x3-6x2+11x+8 so that it is completely divisible by 1-3x +x2

Mathematics
1 answer:
yanalaym [24]3 years ago
5 0

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;

{\left ({x^{3}-6x^{2}+11x+8}  \right )\div 1 - 3x + x^{2}} = 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.

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