When factored completely, m^5 + m^3 -6m is equivalent to what

When factored completely, is equivalent to

To factorize the polynomial

notice that the GCF of each term is m. So we can factorize m out of each term as follows

the fourth-degree polynomial in the brackets an be treated as a quadratic polynomial

and factorized as such. The quadratic has the constant term . We have to look for factors of that add up to  (the co-efficient of the term).

The factors that satisfy the condition are and . So we can factorize the fourth-degree polynomial as

We have factorized the polynomial so far as

But the factor is a difference of two squares and can be factorized as

Our final factored polynomial is

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