Factor the trinomial, if possible: 6r^2 + 5rp -21p

Question

HELP ME THIS IS SO HARD THANK YOU

Answer 1

6r² + 5rp - 21p²

 

You want two numbers that multiply to give 6*(-21) = -126 and add to give 5.  Answer is 14 and -9 (14*(-9) = -126 and 14 + (-9) = 14 - 9 = 5).

 

     6r² + 5rp - 21p²

     6r²  + 14rp - 9rp - 21p²

 

Group terms:

 

    (6r² + 14rp) - (9rp + 21p²)

 

Factor the greatest common factor out of each expression in parentheses:

 

     2r(3r + 7p) - 3p(3r + 7p)

 

Factor out the common factor (3r+7p):

 

     (2r - 3p)(3r + 7p)

 

and we're done!