Question 215465
Factor: {{{3x^2-19x-40}}}


{{{3x^2-19x-40}}}


Step 1.  Need to find two integers m and n where the product is mn=3*(-40)=-120 and their sum m+n=-19.


Step 2.  After several tries, the numbers are -24 and 5.  


Step 3.  Substitute {{{-19x=-24x+5x}}} into {{{3x^2-19x-40}}} and group terms as follows:


{{{(3x^2-24x)+(5x-40)}}}


Step 4.  Factor the first and second group with parenthesis.


{{{(3x^2-24x)+(5x-40)=3x(x-8)+5(x-8)}}}


Step 5.  Now factor out x-8 in both groups since it's a common factor.


{{{(3x^2-24x)+(5x-40)=(x-8)(3x+5)}}}


Step 6.  ANSWER:  {{{3x^2-19x-40=(x-8)(3x+5)}}}


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J