How would you solve this problem?

Question

My textbook has the problem (10y^4+3y^2-7)(2y^2-1)^-1 The only problem is that it says to use synthetic division.  I have learned that this problem should be impossible to solve with synthetic division because when you put the divisor to zero you could get +1 or -1.  My math teacher doesn't understand either.  Can I have some help?

Answer 1

The key is that y only ever appears to even powers.  The numerator and denominator are really polynomials in y^2.  If we let z=y^2, then you want to do the division (10z^2+3z-7)/(2z-1).  Now the denominator is linear and synthetic division does apply.

 

After you divide, substitute y^2 back for z.