In previous sections we showed that when you multiply two
binominals you get a trinomial.
We have also shown how we can factorize a polynomial by finding
a common factor among all terms. If we look at the example above we
see a trinomial that does not have a common factor, but it could
still be factorized by reversing the process.
We can factorize all trinomials of the form
by making them into a product of two binomials
If we use the trinomial from the example above:
We know that we have to find two factors of -6 whose sum is
It's a good idea to make a table to test all combinations
We see that if m = 2 and n = -3 than we will get the correct
There is a pattern that could be good to know so that you don't
have to try all different combinations of values for m and n.
If both b and c are positive then both m and n are positive.
If b is negative whereas c is positive then both m and n are
If c is negative then m and n do not have the same sign.
In the previous section we showed you some special patterns that
could help you when you're simplifying polynomials. The same
patterns can be used to help you when you're factorizing
The difference of two squares pattern is the opposite to the sum
and difference pattern
If we use this as an example:
The perfect square trinomial pattern is the opposite of the
square of a binomial pattern
An example of this would be
Video lesson: Factor the following