I am guessing there are going to be LONG answers...

I am absolute horse (@#&*&E%^& with long division, and I'm working with polynomials here, so...

Here's the example that tells me how to do it. Divide 4x^2+23x-16 by x+5. The solution found is 4x+3 with remainder -31.

I try the problem I have to do. Divide 3x^2-29x+56 by x-7. I do exactly that and come up with 3x-22 with remainder -98. The teacher says this answer is completely wrong!

My math was this:

__3x-22________

x-7|3x^2-29x+56

__-3x^2-7x__

0-22x+56

__-22x+154__

0-98

How did I manage to fail, and what was the correct answer???

OfficialBubbleTanks
Nov 27, 2017

#1**+3 **

I immediately see an issue here!

\(\hspace{26mm}3x\\ x-7\overline{)3x^2-29x+56}\\ \hspace{12mm}3x^2-\textcolor{red}{21x}\\ \hspace{10mm}\overline{\quad\quad\quad\quad\quad}\\ \hspace{15mm}0\hspace{1mm}-\hspace{3mm}8x\)

See if you can finish it from here.

TheXSquaredFactor
Nov 27, 2017

#5**+3 **

You did not completely distribute the 3x to every term in your divisor, which is a common error that can result from a lack of concentration or attentiveness. You seem to understand the process (based on your above work), so continue practicing until you master it. For long division, I would recommend checking your math frequently during long division to ensure no errors are made. Once one error is made, it flows through until the end. Also, it may be difficult to spot an error after finishing because of sensory overload.

TheXSquaredFactor
Nov 27, 2017