How do you factor 18x3-39x2-15x?

Answer 1

18xxx-39xx-15x

Factor out common factor (3x)

3x(6xx-13x-5x)

axx+bx+c

3x(6xx-13x-5)

a=6

b=-13

c=-5

Multiply a and c:

6*-5=-30

Find multiples of ac that add up to b (d,e [ie de=ac, d+e=b]):

-30=-1*2*3*5

-30=-1*30, 1*-30

-30=-2*15, 2*-15

-30=-3*10, 3*-10

-30=-5*6, 5*-6

Rewrite axx+bx+c into axx+dx+ex+c:

3x(6xx-13x-5)

3x(6xx+x-30x-5)

Factor sets of terms (ie axx+dx, and ex+c):

3x(6xx+x-30x-5)

3x(x(6x+1)-5(6x+1))

Combine like terms:

3x(x(6x+1)-5(6x+1))

3x(x-5)(6x+1)