Factoring Polynomials and factoring techniques

Solid8Snake · #1 $Old$ August 22nd, 2009, 12:45 PM

Hello I have come across 4 questions that I simply can't solve with ease, I don't know if there is a universal factoring technique that I am unfamiliar with, but the process of solving the question seems very long and I would like to seek assistance in order to determine whether or not what I am doing is right or wrong. Thank You for your assistance and cooperation.

skeeter · #2 $Old$ August 22nd, 2009, 12:54 PM

start by factoring out the common factor ...

$3(5-2x)\textcolor{red}{(7x-8)^2} - 2\textcolor{red}{(7x-8)^3}$

$\textcolor{red}{(7x-8)^2}[3(5-2x) - 2(7x-8)]$

distribute and combine like terms in the [brackets] ...

$\textcolor{red}{(7x-8)^2}[15-6x-14x+16]$

$(7x-8)^2(31 - 20x)$

follow the same procedure with the other expressions

Solid8Snake · #3 $Old$ August 22nd, 2009, 12:57 PM

Thank you very much, that was much simpler than I expected. I was unfolding the whole thing which made it take very long.