Question 575714
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 25x^2\ +\ 10x\ +\ 1]


Remember using FOIL to multiply two binomials?


The high order term in your product is always the product of the two first terms in the two binomials.  So, how many ways are there to make *[tex \LARGE 25x^2]?


There are only two ways to do it:  *[tex \LARGE 25x\ \cdot\ x] or *[tex \LARGE 5x\ \cdot\ 5x].


Likewise, the constant term in your trinomial is the product of the two 2nd terms in the two binomials.  How many ways are there to make 1 as a product of two integers?  Just 1, namely 1 times 1.


So there are really only two possibilities for the factorization of


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 25x^2\ +\ 10x\ +\ 1]


Either:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (25x\ +\ 1)(x\ +\ 1)]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (5x\ +\ 1)(5x\ +\ 1)]


Multiply them out and see which one works.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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