SOLUTION: solve the following in synthetic division
2x^2+10x+12/x+3
2x^4+x^3-5x^2-9/x+2
x^3-3x^2+12/x+2
3x^4-4x^3+5x^2-7x-5/x-2
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-> SOLUTION: solve the following in synthetic division
2x^2+10x+12/x+3
2x^4+x^3-5x^2-9/x+2
x^3-3x^2+12/x+2
3x^4-4x^3+5x^2-7x-5/x-2
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Let's simplify this expression using synthetic division
Start with the given expression
First lets find our test zero:
Set the denominator equal to zero
Solve for x.
so our test zero is -3
Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.
-3
|
2
10
12
|
Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 2)
-3
|
2
10
12
|
2
Multiply -3 by 2 and place the product (which is -6) right underneath the second coefficient (which is 10)
-3
|
2
10
12
|
-6
2
Add -6 and 10 to get 4. Place the sum right underneath -6.
-3
|
2
10
12
|
-6
2
4
Multiply -3 by 4 and place the product (which is -12) right underneath the third coefficient (which is 12)
-3
|
2
10
12
|
-6
-12
2
4
Add -12 and 12 to get 0. Place the sum right underneath -12.
-3
|
2
10
12
|
-6
-12
2
4
0
Since the last column adds to zero, we have a remainder of zero. This means is a factor of
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