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Section 1.5 : Factoring Polynomials
15. Factor the following polynomial.
\[81{x^2} - 36x + 4\] Show SolutionWe can do this in the manner of the previous problems if we wanted to. On the other hand we can notice that the constant is a perfect square and the coefficient of the \({x^2}\) is also a perfect square. We can also notice that that \(2\left( 9 \right)\left( 2 \right) = 36\) and so we can see that this is one of the special forms.
Therefore, the factoring of this polynomial is,
\[81{x^2} - 36x + 4 = \require{bbox} \bbox[2pt,border:1px solid black]{{{{\left( {9x - 2} \right)}^2}}}\]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.