This is a free lesson from our course in Algebra II
In this lesson you'll learn how to divide a polynomial by something more complicated
than just a simple monomial. Here you'll need to use a different method for
the simplification, what is known as 'polynomial long division'. It works similar to like the
long (numerical) division you learnt earlier, except that now you'll be dividing
with variables. All this is explained including some examples
presented by the instructor with the help of video, and in own handwriting and you
will realize how incredibly simple it is.
Simply saying long division is an algorithm for dividing two numbers, obtaining the quotient
one digit at a time. In algebra, polynomial long division is an algorithm for dividing
a polynomial by another polynomial of the same or lower degree.
(More text below video...)
(Continued from above)
For example, division of polynomial x^{2}
+ 2x + 17 by (x  3), simplifies to quotient = x + 5
and remainder = 32. For any polynomials f(x) and g(x), with g(x) not identical to zero, there exist unique polynomials q(x) and r(x) such that
f(x) = q(x)g(x) + r(x)
with r(x) having smaller degree than g(x).
Polynomial long division finds the quotient q(x) and remainder r(x) given a numerator f(x) and nonzero denominator g(x). The problem is written down like a regular (nonalgebraic) long division problem:
All terms with exponents less than the largest one must be written out explicitly, even if their coefficient are zero.
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