Synthetic Division

M

masters

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Mar 30, 2007
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Synthetic division works well if the coef. of the variable in the divisor is 1. It gets a little more tedious when it's not. But I have a different kind of problem. Here it is:

(10y^4 + 3y^2 - 7) / (2y^2 - 1)

Long division works fine. I have no idea where to start when using synthetic division. How about a hint?
 
masters said:
Synthetic division works well if the coef. of the variable in the divisor is 1. It gets a little more tedious when it's not. But I have a different kind of problem. Here it is:

(10y^4 + 3y^2 - 7) / (2y^2 - 1)

Long division works fine. I have no idea where to start when using synthetic division. How about a hint?
Click to expand...

Go to:

http://www.purplemath.com/modules/synthdiv.htm

for a refresher.
 
I don't have a problem with synthetic division. I can do it when the coef. of the variable in the divisor is 1 or any other number. This problem here is unique in that the coef. of the var. of the divisor is 2 and the variable y is in the 2nd degre. That's the problem.
 
Why don't you substitute

u = 2y^2

Do the division and then substitute back for 'u'.
 
You can't substitute a u for 2y^2. You have to have the same variable in the divisor that you have in the dividend. In long polynomial division,

(10y^4 + 3y^2 -7) / (2y^2 - 1) is equal to 5y^2 + 4 - 3/(2y^2) - 1

Long division is a piece of cake. Synthetic division is a piece of cake so long as the divisor is in the form x - c. It's a little tougher if the divisor is in the form ax - c, where a and c are integers and a>0.

But what if the divisor is in the form ax^n - c?

Using my problem above, and using synthetic division instead of long division, what would be the divisor, and what would be the dividend? That's my question. I can handle it after that.

Thanks.
 
You have to have the same variable in the divisor that you have in the dividend.
Click to expand...

Sooo...?! (Apply any substitution you do to BOTH the Numerator and Denominator.)

Hope that helps.
 
Ok, that did it. This division was far more complicated than using long division, but now I understand. Thanks.
 
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