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mikejoyce · Jun 20, 2009, 06:00 PM

How would I factor the following polynomial and show all of the work?
4x to the second power + 81 - 36x

Perito · Jun 20, 2009, 06:09 PM

$4x^2 -36x + 81$

Note that 81 is a perfect square, and so is 4. Calculate their square roots and use those numbers as possible factor coefficients.

Note the signs of the three coefficients in the equation (+, -, +). Because the middle coefficient is negative and the other coefficients are positive, you'll have to factor like this:

$(ax-b)(cx-d)$ where $b d = 81$ and $a c = 4$ . Note that b and d may be the same number and a and c may be the same number.

also, you have to select these coefficients in such a way that $ad + bc = -36$ .

Think about it. The solution is pretty easy.