Question 214295
Factor the trinominal


{{{2(m+p)^2-7(m+p)-30}}}


Step 1.  Let x=m+p, then


{{{2x^2-7x-30}}}


Step 1.  We need to find two integers A and B that A*B=ac and A+B=b where 


{{{ax^2+bx+c}}} in order to be factorable and a=2, b=-7 and c=-30


Step 2.  In the above example, then A*B=-60 and A+B=-7.  


Step 3.  After trial and error the numbers are A=-12 and B=5


Step 4.  Using step 3, we can use grouping as follows 


{{{2x^2-7x-30=2x^2-12x+5x-30}}}  where {{{-7x=-12x+5x}}}


{{{2x^2-7x-30=(2x^2-12x)+(5x-30)}}}


Step 5.  Factor out 2x in first group and 5 in second group


{{{2x^2-7x-30=2x(x-6)+5(x-6)}}}


Step 6.  Factor out (x-6) since it is common in both groups.


{{{2x^2-7x-30=(2x+5)(x-6)}}} 


We can use the FOIL method to verify


{{{2x^2-7x-30=2x^2-12x+5x-30=2x^2-7x-30}}}


Step 6. Now substitute back x=m+p to {{{2x^2-7x-30=(2x+5)(x-6)}}} to get



{{{2(m+p)^2-7(m+p)-30=(2(m+p)+5)(m+p-6)}}}  (ANSWER)


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J