How to factor 5m^2+15m-20 step by step

Key concept: Some trinomials look harder than they are because the first move is not a trinomial method at all — it is usually the greatest common factor. That small step makes the rest much cleaner.

Step by step

Start with

$5m^2+15m-20$

Step 1: Factor out the GCF

All terms are divisible by $5$:

$5(m^2+3m-4)$

Step 2: Factor the trinomial inside the parentheses

We need two numbers that multiply to $-4$ and add to $3$.

Those numbers are $4$ and $-1$.

So,

$m^2+3m-4=(m+4)(m-1)$

Final answer

$\boxed{5(m+4)(m-1)}$

Pitfall alert

A frequent slip is trying to factor $5m^2+15m-20$ directly and ignoring the common factor of $5$. If you skip that step, the numbers get messier for no good reason.

Try different conditions

If the expression were $5m^2+15m+20$, the inside trinomial would be $m^2+3m+4$, which does not factor over the integers. The sign of the constant term changes the whole picture.

Further reading

greatest common factor, trinomial factoring, integer factors