 # Factor Trinomials by GCF

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More lessons for factoring and other Grade 9 topics

When factoring trinomials, the first 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 – 4p3q = 2pq(1 + 3p – 2p2) ← extract GCF 2pq

How to factor trinomials with a negative leading coefficient?
Factor trinomial with negative in front.
Example:
Factor: -30x2 + 7x + 4
How to factor a trinomial with negative leading coefficient?
Example:
Factor: -6x2 - x + 7
How to find common factors as a first step in factoring a quadratic equation?
Factor: 5w2 - 20w - 160
How to factor the greatest common factor (gcf) from a polynomial?
Factor: 4x3 - 2x2 + 6x

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