Question 452963
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I am having a problem factoring this one 14a^2-45a-14.
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        The standard treatment of this problem and many other similar problems is to find 

        the roots of a polynomial and then to decompose the polynomial.

        @mananth in his post started the job, but not completed it, so I came to do everything 

        from the beginning to the end.



<pre>
Find the roots of the given polynomial using the quadratic formula

    d = b^2 - 4ac = 45^2 - 4*14*(-14) = 2809

    {{{x[1]}}} = {{{(-b + sqrt(d))/(2a)}}} = {{{(-(-45) + sqrt(2809))/28}}} = {{{(45+53)/18}}} = {{{98/28}}} = {{{7/2}}};

    {{{x[2]}}} = {{{(-b - sqrt(d))/(2a)}}} = {{{(-(-45) - sqrt(2809))/28}}} = {{{(45-53)/18}}} = {{{-8/28}}} = {{{-2/7}}}.


Therefore, the decomposition of our polynomial is

    14a^2 - 45a - 14 = {{{14*(a-7/2)*(a+2/7)}}} = (2a-7)*(7a+2).


<U>ANSWER</U>.  14a^2 - 45a - 14 = (2a-7)*(7a+2).
</pre>

Solved.