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.

Find the Greatest Common Factor - GCF

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 + 6p²q - 4 p³q

Solution:

a) ad + dc + df = d(a + c + f ) ← extract GCF d

b) 2pq + 6p²q - 4 p3q = 2pq(1 + 3 p - 2 p²) ← 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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