X3+7x2+16x+12/x3+5x2+8x+4

Предыдущий
вопрос Следующий
вопрос

To divide the polynomials, we can use long division or synthetic division. Here, I'll show the steps using long division:

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x^2 + 2x + 3 | x^3 + 5x^2 + 8x + 4

First, we divide x^3 by x^2 to get x, which we write above the line. Then, we multiply the divisor x^2 + 2x + 3 by x to get x^3 + 2x^2 + 3x. We then subtract this from the dividend:

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x^2 + 2x + 3 | x^3 + 5x^2 + 8x + 4
-(x^3 + 2x^2 + 3x)
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3x^2 + 5x + 4

Next, we bring down the next term, which is 4. Now, we divide 3x^2 by x^2 to get 3, which we write above the line. Then, we multiply the divisor x^2 + 2x + 3 by 3 to get 3x^2 + 6x + 9. We then subtract this from what we have so far:

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x^2 + 2x + 3 | x^3 + 5x^2 + 8x + 4
-(x^3 + 2x^2 + 3x)
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3x^2 + 5x + 4
-(3x^2 + 6x + 9)
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-x - 5

Finally, we have -x - 5 as our remainder. Therefore, the result of the division is:

x + 3 - (x + 5) / (x^2 + 2x + 3)