
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 21st, 2015, 10:05 PM  #1 
Newbie Joined: Jun 2015 From: Philippines Posts: 1 Thanks: 0  Long Division and Synthetic Division
Hi I have an homework which is I'm having hardtime to solve. 1.) Long Division 6a^4  43a^2b^2 + 7a^2b  9ab^3  5b^4 ÷ 3a^2 + 5ab  7b^2 2.) Synthetic Division 2x^5 + x^4 + 4x^3 + x + 1 ÷ x + 1/2 
June 22nd, 2015, 12:07 AM  #2 
Senior Member Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 155 Math Focus: Abstract algebra 
I think there is a typo in the first question: It should be 1) $\displaystyle \frac{6a^4  43a^2b^2 + 7a^{\color{red}3}b  9ab^3  5b^4}{3a^2 + 5ab  7b^2}$This would then be homogeneous in $a$ and $b$ (meaning the sum of the powers of $a$ and $b$ is constant in the numerator and denominator (separately)) so you can reduce it to an expression in just one variable: Factor out the highest power of $b$ in the numerator and the highest power of $b$ in the denominator, and let $x=\dfrac ab$. $\displaystyle \frac{6a^4  43a^2b^2 + 7a^3b  9ab^3  5b^4}{3a^2 + 5ab  7b^2}$$\displaystyle =\ \frac{b^4\left[6\left(\frac ab\right)^443\left(\frac ab\right)^2+7\left(\frac ab\right)^39\left(\frac ab\right)5\right]}{b^2\left[3\left(\frac ab\right)^2+5\left(\frac ab\right)7\right]}$ $\displaystyle =\ b^2\cdot\left[\frac{6x^443x^2+7x^39x5}{3x^2+5x7}\right]$ And now you can apply longdivision techniques, substituing $x$ back to $a$ and $b$ in the end. This is assuming there is a typo and the way I fixed it above is correct. If there is no typo, then...I don't know. 

Tags 
division, long, synthetic 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
synthetic division  oti5  Algebra  5  March 19th, 2012 07:40 AM 
Synthetic Division Problem  Kodwo  Algebra  7  August 7th, 2011 04:01 PM 
Long Division  MathematicallyObtuse  Algebra  4  November 2nd, 2010 06:27 PM 
Synthetic Division  symmetry  Algebra  3  February 18th, 2007 06:02 PM 
Synthetic Division Problem  Kodwo  Abstract Algebra  0  December 31st, 1969 04:00 PM 