divide (x^2 - 10x+30) ÷ (x-5)
To divide the polynomial (x^2 - 10x + 30) by (x - 5), we can use polynomial long division.
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(x - 5) | x^2 - 10x + 30
To start, we divide x by x, which gives us x. We then multiply (x - 5) by x to get x^2 - 5x, and subtract it from x^2 - 10x + 30.
x^2 - 10x + 30
- (x^2 - 5x)
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-5x + 30
From here, we divide -5x by x, which gives us -5, and multiply (x - 5) by -5 to get -5x + 25. We then subtract it from -5x + 30.
x^2 - 10x + 30
- (x^2 - 5x)
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-5x + 30
- (-5x + 25)
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5
Finally, we divide 5 by x and get 5/x. Since there are no more terms to bring down, the division is complete.
Thus, (x^2 - 10x + 30) ÷ (x - 5) = x - 5 + 5/(x - 5).