Question 805197: How to divide this using synthetic division?
(X^3-5x^2-7x+25)/(x-5)
Answer by coolcat!!!(1)   (Show Source):
You can put this solution on YOUR website! You take (x-5) and take out the 5
So: (x-5) => x=5
You must then take only the coefficients of all the x's and the constant:
X^3-5x^2-7x+25 => 1 -5 -7 25
5 | 1 -5 - 7 25
| 5 0 -35
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1 0 -7 -10
Explanation: you write the coefficients/constant in a line at the top, and then draw a vertical line on the left of the numbers, and -leaving some space- on horizontally under the numbers.
Write what dividing by (the 5) on the left side of the vertical line. YOUR READY TO SYNTHETICALLY DIVIDE.
That first number (the 1) is just brought down, so you write it under the horizontal line.
Now, 1 times the number you are dividing (5) is 5. So place that between the numbers you initially had written and the horizontal line. Now, you must ADD that -5 and 5. So it is now 0.
0 times the number you are dividing (5) is 0. Put the 0 under the next number in the line (-7). Now you ADD -7 and 0, which is -7. -7 times 5 is -35. Place -35 under the 25.
Finally, the 25 plus -35 is -10.
In conclusion, taking the numbers 1 0 -7 -10,
the quotient is x^2-7 R: -10
The 1 is just the x^2 , the zero is 0x (so we don't write it) the -7 is the constant, and -10 is the remainder.
We start with x^2 because the quotient has one less exponent at it's first x, than the initial equation that which we divided by (x-5) (because it was x^3.
Hope this helped! Good luck!
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