* If a binomial is both difference of squares and
cubes we must factor it as
difference of squares first to obtain a more complete factorization.
* Not all polynomials factor over the real numbers, in this case,
Algebra students can simply write “does not factor.”
Certainly we could check to see if the given solutions
solve the quadratic equations we
came up with.
If we are asked to solve an absolute value equation,
lXl=n, we first isolate the absolute
value then set the argument X equal to ±n. We have seen this technique before
difference here is that the resulting equations may be quadratic.
The technique for solving rational equations is the
same as well, multiply both sides by
the LCD and clear the fractions keeping a close eye on the restrictions.
Dividing by zero is undefined, with this in mind, whenever we see a variable in
denominator of an expression we need to consider that the variable could be a
that makes the denominator zero . A restriction on the variable is noted
so that the
variable in the denominator can not be assigned that value. If a solution to a
equation turns out to be a restriction, simply throw it away. Do not include it
in the solution set.
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