Divide (x3 – 8x2 + 17x – 10) ÷ (x – 5)
To divide (x3 – 8x2 + 17x – 10) ÷ (x – 5), we can use long division:
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x - 5 | x3 – 8x2 + 17x – 10
First, we divide x into x3, which gives us x2:
x2
Then we multiply (x – 5) by x2, which gives us x3 – 5x2:
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x - 5 | x3 – 8x2 + 17x – 10
x3 – 5x2
_____________
Next, we subtract (x3 – 5x2) from (x3 – 8x2) to get -3x2:
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x - 5 | x3 – 8x2 + 17x – 10
x3 – 5x2
_____________
- 3x2
We bring down the next term, which is 17x:
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x - 5 | x3 – 8x2 + 17x – 10
x3 – 5x2
_____________
- 3x2
+ 17x
Then we divide x into -3x2, which gives us -3x:
________________________
x - 5 | x3 – 8x2 + 17x – 10
x3 – 5x2
_____________
- 3x2
+ 17x
___________
-3x
We multiply (x – 5) by -3x, which gives us -3x2 + 15x:
________________________
x - 5 | x3 – 8x2 + 17x – 10
x3 – 5x2
_____________
- 3x2
+ 17x
___________
-3x2 + 15x
Next, we subtract (-3x2 + 15x) from (-3x2 + 17x) to get 2x:
________________________
x - 5 | x3 – 8x2 + 17x – 10
x3 – 5x2
_____________
- 3x2
+ 17x
___________
-3x2 + 15x
- (-3x2 + 15x)
___________
2x
Lastly, we bring down the last term, which is -10, and divide x into 2x, which gives us 2:
________________________
x - 5 | x3 – 8x2 + 17x – 10
x3 – 5x2
_____________
- 3x2
+ 17x
___________
-3x2 + 15x
- (-3x2 + 15x)
___________
2x
- 2
___________
-12
Thus, (x3 – 8x2 + 17x – 10) ÷ (x – 5) = x2 - 3x + 2 with a remainder of -12.