In the same way as you could factor trinomials on the form
You can factor polynomials on the form of
If a is positive then you just proceed in the same way as you
did previously except now
We can see that c (-8) is negative which means that m and n does
not have the same sign. We now want to find m and n and we know
that the product of m and n is -8 and the sum of m and n multiplied
by a (3) is b (-2) which means that we're looking for two factors
of -24 whose sum is -2 and we also know that one of them is
positive and of them is negative.
This means that:
We can then group those terms that have a common monomial
factor. The first two terms have x together and the second two -2
and then factor the two groups.
Notice that both remaining parenthesis are the same. This means
that we can rewrite this using the distributive propertyit as:
This method is called factor by grouping.
A polynomial is said to be factored completely if the polynomial
is written as a product of unfactorable polynomials with integer
Video lesson: Factor the following