Factor Trinomials by GCF
When factoring trinomials, the fisst step would be to try to find the greatest common factor (GCF). We can then pull out the GCF by using the distributive property in reverse.
We can factor trinomials by first looking for factors that are common (that is the GCF)
Example:
Factor the following trinomials:
a) ad + dc + df
b) 2pq + 6p 2 q - 4 p 3 q
Solution:
a) ad + dc + df = d (a + c + f ) ← extract GCF d
b) 2pq + 6p 2 q - 4 p 3q = 2pq (1 + 3 p - 2 p 2 ) ← extract GCF 2pq
The following two videos show how to factor trinomials with a negative leading coefficient.
Factor trinomial with negative in front
Factor trinomial with negative leading coefficient
The following video shows an example of finding common factors as a first step in factoring a quadratic equation.
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