distribute the negative sign to both terms. –(2x^2 – 6x) = – 2 x + 6x. Then draw
another line and combine terms. The 2x^2 and the –2x^2 will cancel, leaving just an
x. Bring down the last term of the polynomial, the –1, and put it next to the x.
That gives us:
From here, you repeat the whole process, but divide your x – 3 into
whatever’s below the line, instead of the initial dividend. So now you’re going to
divide x – 3 into x – 1. x/x = +1, so put that up top next to your quotient 2x,
making a quotient of 2x + 1. Multiply the 1 back into x – 3 and subtract, giving
you:
Now at this point, all you have left is just a measly little 2. You might think:
“How can I divide x + 3 into 2? x doesn’t go into 2 at all because it’s just a
constant!” But not to fear—you don’t really have to figure out the division. In
polynomial division, this is the remainder. This is exactly the same situation at
the end of long division with numbers—like if you tried to divide the number 5
into 8 and had 3 left over. You can’t divide 5 into 3, so you write the quotient as
a fraction with the remainder in the numerator and the divisor in the
denominator, giving you . You’re going to do exactly the same thing with
your polynomial! Take the remainder and put it over the divisor, like this: .
This will be the extra little piece you stick at the end of your quotient polynomial
to give the full quotient and remainder: