SOLUTION: y^3-13y^2+54y-72 ___________ _____ y-6

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Question 119792: y^3-13y^2+54y-72
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y-6
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Note: I'm going to use "x" instead of "y"



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 6


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.
6|1-1354-72
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
6|1-1354-72
|
1

Multiply 6 by 1 and place the product (which is 6) right underneath the second coefficient (which is -13)
6|1-1354-72
|6
1

Add 6 and -13 to get -7. Place the sum right underneath 6.
6|1-1354-72
|6
1-7

Multiply 6 by -7 and place the product (which is -42) right underneath the third coefficient (which is 54)
6|1-1354-72
|6-42
1-7

Add -42 and 54 to get 12. Place the sum right underneath -42.
6|1-1354-72
|6-42
1-712

Multiply 6 by 12 and place the product (which is 72) right underneath the fourth coefficient (which is -72)
6|1-1354-72
|6-4272
1-712

Add 72 and -72 to get 0. Place the sum right underneath 72.
6|1-1354-72
|6-4272
1-7120

Since the last column adds to zero, we have a remainder of zero. This means is a factor of

Now lets look at the bottom row of coefficients:

The first 3 coefficients (1,-7,12) form the quotient




So

You can use this online polynomial division calculator to check your work

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