Question 753968
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Take out an *[tex \LARGE a]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\left(10a^2\ +\ 17a\ +\ 3\right)]


Multiply the lead coefficient on the quadratic trinomial by the constant:  10 times 3 is 30.  Find two factors of 30 that add  up to 17.  Try 15 and 2.


Split the first degree term into two parts, *[tex \LARGE 15a] and *[tex \LARGE 2a]


Group the factors into pairs:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\left(\left(10a^2\ +\ 15a\right)\ +\ \left(2a\ +\ 3\right)\right)]


Factor out *[tex \LARGE 5a] from the first pair of factors:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\left(5a\left(2a\ +\ 3\right)\ +\ \left(2a\ +\ 3\right)\right)]


Factor out 1 from the second pair


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\left(5a\left(2a\ +\ 3\right)\ +\ 1\left(2a\ +\ 3\right)\right)]


Factor out *[tex \LARGE (2a\ +\ 3)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\left(5a\ +\ 1\right)\left(2a\ +\ 3\right)]



John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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