Using Long Division with Polynomials (4.1.1) Flashcards
• Division for polynomials follows the same procedures as long division with numbers. To divide polynomials, follow the
same steps you used for elementary school long division
• Division for polynomials follows the same procedures as long division with numbers. To divide polynomials, follow the
same steps you used for elementary school long division
• When setting up your polynomial division problems, be sure to arrange the dividend (the divided number) with the powers
of the terms in descending order. If any power is missing, insert its term with a 0 coefficient.
• When setting up your polynomial division problems, be sure to arrange the dividend (the divided number) with the powers
of the terms in descending order. If any power is missing, insert its term with a 0 coefficient.
• Your remainder is always less than your divisor, or you could keep dividing.
• Your remainder is always less than your divisor, or you could keep dividing.
Any fraction is a division problem with the divided number,
or dividend, as the numerator, and the dividing number, or
divisor, as the denominator.
In this case, the f(x) matches the 103 in the fraction, and it
gets divided into. The g(x) matches the 3 in the fraction, and
it does the dividing. The q(x) matches the 34 in the fraction
problem, and is the answer (quotient).
Note: The original dividend can be recreated by multiplying
the quotient with the divisor and adding the remainder to that
product. This is your way to check your division answer for
accuracy.
Another way to express the quotient and remainder is as the
sum of the quotient and the remainder divided by the divisor.
In this example, first set up the long division problem and
include 0x
3
as a place.
Next, figure what multiplies with x
2 to produce x
4
. Since x
2
is the answer, write x
2
on the answer line then multiply x
2
by
the divisor.
Subtract x
4
+3x
3
–5x
2
from the dividend and bring down the
next term to be divided.
Repeat the process:
· What term multiplies with x
2
to give –3x
3
?
· Multiply –3x by the divisor.
· Subtract and bring down the last term in the dividend
Again, repeat the process: · What term multiplies with x 2 to give 17x 2 ? · Multiply 17 by the divisor. There are no more terms in the dividend, so the process is complete The leftover expression, –72x + 75, is the remainder.
Any fraction is a division problem with the divided number,
or dividend, as the numerator, and the dividing number, or
divisor, as the denominator.
In this case, the f(x) matches the 103 in the fraction, and it
gets divided into. The g(x) matches the 3 in the fraction, and
it does the dividing. The q(x) matches the 34 in the fraction
problem, and is the answer (quotient).
Note: The original dividend can be recreated by multiplying
the quotient with the divisor and adding the remainder to that
product. This is your way to check your division answer for
accuracy.
Another way to express the quotient and remainder is as the
sum of the quotient and the remainder divided by the divisor.
In this example, first set up the long division problem and
include 0x
3
as a place.
Next, figure what multiplies with x
2 to produce x
4
. Since x
2
is the answer, write x
2
on the answer line then multiply x
2
by
the divisor.
Subtract x
4
+3x
3
–5x
2
from the dividend and bring down the
next term to be divided.
Repeat the process:
· What term multiplies with x
2
to give –3x
3
?
· Multiply –3x by the divisor.
· Subtract and bring down the last term in the dividend
Again, repeat the process: · What term multiplies with x 2 to give 17x 2 ? · Multiply 17 by the divisor. There are no more terms in the dividend, so the process is complete The leftover expression, –72x + 75, is the remainder.
