Work A Divison Problem
This program lets you practice long division of polynomials.
The problems all have a binomial of degree one for their divisor. The dividends are random polynomials of degree three to five.
There are four steps in the long division process that repeat until the problem is complete.
1.Divide:We divide the highest remaining term in the dividend by the divisor.
We get this answer by looking at the hightest term in the divisor and divide the highest remaining term in the dividend by it. For ecample if 4x3 is the highest remaining term in the dividend and the divisor is 2x-1, we divide 4x3 by 2x and get 2x2. We put that number above the 4x3 above the division line.
2.Multiply:We multiply the answer we got in the first step by the divisor and get
4x4-2x3. We place this below the last partial dividend we have.
3.Subtract:We substract the partial result we just got from the partial dividend above it.
4.Subtract:. We write the next power of the polynomial next to the subtraction we have just done.
The x4 goes away and we are left with an x3 term as the highest remaining one.
Now we 'bring down' the x2 term from the original problem and repeat the three steps above.
We are done when the highest term of remaining dividend is less than the highest power of the divisor. In this case, the remainder is just a number.
We check by multiplying the answer by the divisor and adding the remainder. We should get the original dividend.
What we are doing
In the case of polynomial division we are simply doing the division one term at a time. The
process is a little more complicated than we would like, because we have a remainder at each stage
that needs to be incorporated in the division problem we are working at the next step.
If you want to feel more comfortable about this, think back to how we learned to do long division in grade school.
We would do the division one digit at a time. We would divide the first digit by the divisor, multiply the answer by the divisor,
and then subtract to get a remainder. In the next step, we would bring down the next digit and divide these two
numbers by the divisor. We were done when there was nothing left to bring down. The remainder was
the result of the last subtraction we had done.