How do I factor this expression? 6x^2+7x-20. I know the answer is (3x - 4)(2x + 5) because I FOILed it, but otherwise, what would I have to do?

Question

anonymous · Answer

the easiest method will be to use the quadratic formula and then work backwards

anonymous · Answer

Thank you so much!

anonymous · Answer

its a pleasure..happy 2 help

anonymous · Answer

How would I factor it after using the quadratic formula? I got -5/2 and 4/3.

anonymous · Answer

then you would work backwards and say one of the factors is $x+\frac{5}{2}$ but instead multiply by 2 and say it is $2x+5$

anonymous · Answer

similarly for $\frac{4}{3}$ you can write 
$$x=\frac{4}{3}\iff x-\frac{4}{3}=0\iff 3x-4=0$$

anonymous · Answer

Thank you! I understand now! (:

anonymous · Answer

sometimes it is easier just to factor, but the quadratic formula always works

anonymous · Answer

yw

campbell_st · Answer

well here is an easy method that works everytime 

for a quadratic 

$$ax^2 + bx + c $$

start my multiplying a and c 

in your question its 6 x -20 = -120

find the factors of -120 that add to 7 

the larger factor is positive the smaller negative 

so its 15 and - 8   

next write 

(ax + factor 1)(ax + factor 2)
--------------------------
                     a

so for your question you have 

(6x + 15)(6x - 8)
----------------
            6

remove common factors from the binomials

3(2x + 5)2(3x - 4)               3*2(2x + 5)(3x -4)
-----------------     =    ------------------
             6                                       6

cancel the common factor leaves 

(2x + 5)(3x -4)

no guessing and no GQF needed.