Question

What must be added to polynomial p(x)=6x^5+5x^4+11x^3-3x^2+x+1 so that the resulting polynomial is exactly divisible by 3x^2-2x+4? (Hint:add-r(x) oro p(x).
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Answer 1

Answer:

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Answer 2

Given polynomial is 6x5+5x4+11x3-3x2+x+1 is divisible by 3x2-2x +4

3x2-2x +4 ) 6x5+5x4+11x3-3x2+x+1 ( 2x3+3x2+3x-3

6x5- 4x4+ 8x3 (subtract)

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9x4+3x3-3x2

9x4-6x3+12x2 (subtract)

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9x3-15x2 + x

9x3- 6x2 +12x (subtract)

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-9x2- 11x + 1

-9x2+ 6x -12 (subtract)

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-17x + 13

∴ Additive inverse of -17x + 13 is 17x - 13

Hence 17x - 3 is added to 6x5+5x4+11x3-3x2+x+1,so that the polynomial so obtained is exactly divisible by 3x2-2x +4