SOLUTION: Divide A. Use long division to divide x³+6x²-x-30 by x²+8x+15 B. Use synthetic division to divide (x³+5x²-18)/(x+3)

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Question 38302: Divide
A. Use long division to divide x³+6x²-x-30 by x²+8x+15

B. Use synthetic division to divide (x³+5x²-18)/(x+3)
Found 2 solutions by Nate, junior403:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
A. Use long division to divide x³+6x²-x-30 by x²+8x+15
%28x%5E3%2B6x%5E2-x-30%29%2F%28x%5E2%2B8x%2B15%29
%28%28x%2B3%29%28x%2B5%29%28x-2%29%29%2F%28%28x%2B3%29%28x%2B5%29%29
x-2
B. Use synthetic division to divide (x³+5x²-18)/(x+3)
x....1....5....0....-18
-3 ! 1 ! 2 ! -6 ! 0
So: x%5E2+%2B+2x+-6

Answer by junior403(76) About Me  (Show Source):
You can put this solution on YOUR website!
A. Use long division to divide x³+6x²-x-30 by x²+8x+15
We set up a long division problem like this...
_______________
x^2+8x+15)X^3+6x^2-x-30
We can now start with the first variable (X^2)and find the value that will make the divisor (x^3) true. (x^2 * x = x^3)
Then multiply that answer by the remaining variables. (x * 8x = 8x^2) and (x * 15 = 15x) Then we distribute a negative to subtract that line from the top line to get a new set of numbers...and repeat.
x^2 multiplied by what makes -2x^2, and so on just like long division w/real numbers...
So...
_______________x_-_2_______
x^2+8x+15)x^3+6x^2 - x -30
________-(x^3+8x^2+15x)
_____________-2x^2-16x -30
____________+2X^2+16X +30
_______________________0
The answer is x-2.
To check, simply multiply x^2+8x+15(x-2) = x^3+6x^2-x-30
Its kind of hard to show all the work here, but I hope you get the idea.
B. Use synthetic division to divide (x³+5x²-18)/(x+3)
This process can be a little tricky.
First we change the x+3 into x-(-3)
Now just write the coefficients of x^3 5x^2 18 with -3 on the left
-3)1 5 18 (set up like long division)
First carry down the 1 by itself.
-3)1 5 18
____________
__1
Then multiply -3(1) and place the answer under the second column.
-3)1 5 18
___-3____
__1
Then subtract...
-3)1 5 18
___-3____
__1_2
then multiply the -3 by that result...
-3)1 5 18
___-3-6
__1_2
And subtract...
-3)1 5 18
___-3-6
__1_2_12 (12 is the remainder, so it is written over the divisor x+3)
Now the result 1 2 12 can take the original signs...
1x + 2 -12/x+3
And this is the final answer...
I hope this helps.
Let me know if you have any further questions about this.
Thanks.
Good Luck!







Good Luck!