Question 214081
Factor completely:


{{{3x^2-13x+14=(3x-7)(x-2)}}}


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=3, b=-13 and c=14


Step 2.  In the above example, then A*B=(3)(14)=42 and A+B=-13.  


Step 3.  After trial and error the numbers are A=-6 and B=-7


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


{{{3x^2-13x+14=3x^2-6x-7x+14}}}  where {{{-13x=-6x-7x}}}


{{{3x^2-13x+14=(3x^2-6x)+(-7x+14)}}}


Step 5.  Factor out 3x in first group and -7 in second group


{{{3x^2-13x+14=3x(x-2)+(-7)(x-2)}}}


Step 6.  Factor out (x-2) since it is common in both groups.


{{{3x^2-13x+14=(3x-7)(x-2)}}}  ANSWER


We can use the FOIL method to verify


{{{(3x-7)(x-2)=3x^2-6x-7x+2*7=3x^2-13x+14}}}


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