Some equations can be put into factored form such that the product of
the factors is zero. Then we can solve by using the fact that if
(a)(b) = 0, then either a or b (or
both) is zero.
Be careful not to make these common
- When solving
do not make the mistake of setting x + 1 =15
and x + 3 = 15. It is not true that
(a)(b) = 15 means that a = 15 or
b = 15 (or both). Thus we have to expand the
left-hand side and set the equation to zero.
- When solving
we might be tempted to divide both sides by x + 3.
However, if we do this we omit the solution x = -3,
because we can't divide by zero.
If we are unable to factor an equation and it is quadratic (the
highest power of the variable is 2) we can use the quadratic
then the solutions are
Solve for x
This is the same as
which we are unable to factor using integers, so we use
Note that we can approximate these with the decimal approximations
We could find these directly from a graph or a calculator.
Be sure you've gone through each step in the examples above before
doing these. Once you've worked them until you're sure that you
understand them, go on to the next section. There are more problems
of this type in the section test at the end of the section.
Note that you can get new practice problems by clicking the "Refresh"
button at the bottom of the practice set.
precal: 7.3 - solving by factoring
page created: Fri May 24 15:30:26 2013
©2003-2007 Gavin LaRose, Pat Shure /
University of Michigan Math Dept. /
Regents of the University of Michigan