Divide the first term in the divisor into the first term in the
dividend. This gives us the first term in the quotient.
Multiply this term in the quotient by the divisor, and subtract
the product from the dividend
When you subtract, remember that subtraction means changing
the sign and adding
Theoretically, you could bring down all the terms from the
divisor into the remainder, but, as we shall see, the next term is the
only one which will come into play at the next step.
Repeat this process with the remainder. Divide the first term in
the divisor into the first term in the remainder. That gives us the
next term in the quotient.
Multiply this next term in the quotient by the divisor, and
subtract from the remainder.
Again, subtract means change the sign and add. When we bring
down the next term it is the last term in the dividend.
Repeat the process again. We can repeat it once more because
there is something you can multiply the first term in the divisor, the
x, by to get the first term in the remainder, the 3x, namely, 3. That is
the next term in the quotient.
We finally get a remainder that has smaller degree than the
divisor. At this point we stop with this quotient and remainder. We
could express our answer as
It is very common to form a fraction by putting the remainder
over the divisor and adding the fraction to the quotient.
These problems can be checked by multiplying the quotient by
and adding the quotient
Notice the relation between the multiplication and division
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