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Section 1.5 : Factoring Polynomials

14. Factor the following polynomial.

\[4{w^2} - 25\] Show Solution

We can do this in the manner of the previous problems if we wanted to. On the other hand we can notice that we have a difference of perfect squares and so this is one of the special forms.

Therefore, the factoring of this polynomial is,

\[4{w^2} - 25 = \require{bbox} \bbox[2pt,border:1px solid black]{{\left( {2w - 5} \right)\left( {2w + 5} \right)}}\]

Note that while you don’t need necessarily need to know the special forms if you do and can easily recognize them it will make the factoring easier.