what must be added to 6x5+5x4+11x3-3x2+x+5 so that it may be divisible by 3x2 -2x+ 4
Answers
Answer:
Step-by-step explanation:
Given
what must be added to 6x5+5x4+11x3-3x2+x+5 so that it may be divisible by 3x2 -2x+ 4
ANSWER
So by dividing we get
3x^2 – 2 x + 4) 6 x^5 + 5 x^4 + 11 x^3 – 3 x^2 + x + 5 (2 x^3 + 3 x^2 + 3 x – 3
6 x^5 – 4 x^4 + 8 x^3
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9 x^4 + 3 x^3 – 3 x^2
9 x^4 – 6 x^3 + 12 x^2
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9 x^3 – 15 x^2 + x + 5
9 x^3 – 6 x^2 + 12 x
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9 x^2 – 11 x + 5
9 x^2 + 6 x – 12
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- 17 x + 17
So we need to add 17 x – 17 to 6 x^5 + 5 x^4 + 11 x^3 – 3 x^2 + x + 5, so that the polynomial is exactly divisible by 3 x^2 – 2 x + 4.