thingsPOLYNOMIAL DIVISION
Another type of problem you might run into involves “dividing polynomials.” If
you consult the table above, you can see that a polynomial is any expression
made up of unlike terms of variable factors (terms are products that are separated
by a + or –). For example, here’s a polynomial: 2x^2 – 5x – 1. Three unlike terms,
separated by addition or subtraction. The SAT might ask you what would result
if you divided that 2x^2 – 5x – 1 by a simpler polynomial, something like x – 3.
They’ll write it like this:
The Serpent expects you to know how to simplify this ratio using something
called “polynomial long division.” Polynomial long division is a lot like regular
long division with numbers, but instead of dividing the digits into each other,
you divide the terms into each other. First write it out in long division form, like
this:
Now, much like you might do if we were working with the digits of numbers
(instead of the terms of polynomials), you’re going to divide the first term of the
divisor polynomial (the x – 3) into the first term of the dividend polynomial (the
2 x^2 – 5x – 1), and write the result on top. How many times does x go into 2x^2 ? If
you divide 2x^2 /x you get 2x. So write that on top. Then multiply each term of the
divisor again by that quotient term, and write the result below. Now you should
have:
Remember that you’re subtracting NEGATIVE 6x from the trinomial, so you are really adding 6x.
—SamanthaNext, you’re going to subtract the 2x^2 – 6x part from the polynomial above.
Remember that you’re subtracting the whole expression so you’ll have to