Question #e7b5e

1 Answer
Nov 9, 2015

x^2 + 4x + 3

Explanation:

Here's what the set up looks like...
1| 1 + 3 -1 - 3

The 1 on the left is the "root" of the bottom, or the number that x would be to make it equal 0. Or you can just think of it is the opposite of the number after x.

All of the numbers after are the coefficients in front of the powers of x in decreasing order.

Now the process. Draw leave some space and draw a line underneath like so...

1| 1 + 3 -1 - 3

-------

Add down and multiply up diagonally by the number in the top left (I hope this makes sense)

1| 1 + 3 -1 - 3
color(white)(Xll) 0color(white)(XXXXXXXXX)<---start with a zero here
-------
color(white)(Xll) 1color(white)(XXXXXXXXX) <--- add down

1| 1 + 3 -1 - 3
color(white)(Xll) 0color(white)(llll) 1color(white)(XXXXXXX)<---multiply up by 1
-------
color(white)(Xll) 1color(white)(Xl)4color(white)(XXXXXX) <--- add down

Here's the rest:
1| 1 + 3 -1 - 3
color(white)(Xll) 0color(white)(llll) 1color(white)(llla) 4color(white)(llla) 3
-------
color(white)(Xll) 1color(white)(Xl)4color(white)(iiia) 3 color(white)(iiia)0

Now use those numbers on the bottom as coefficients for a polynomial with degree one lower than the original numerator:

1x^2 + 4x + 3 + 0/(x-1) (this last term is the remainder, and this is how you write it)

Clean it up...
x^2 + 4x + 3