Factor 3x^2-19x+20

(3x-4) (x-5)

Step-by-step explanation:

This is in the form

ax²+bx+c.

To factor this, we find factors of a·c that sum to b; this means factors of 3 (20) = 60 that sum to - 19:

60 = 1 (60) or - 1 (-60); 2 (30) or - 2 (-30); 3 (20) or - 3 (-20); 4 (15) or - 4 (-15); 5 (12) or - 5 (-12); 6 (10) or - 6 (-10). The only of these that sum to - 19 are - 4 and - 15. This means we will split up - 19x into - 4x and - 15x:

3x²-4x-15x+20

Next we group the first two terms and the last two terms:

(3x²-4x) + (-15x+20)

Factor out the GCF of each group. For the first group, this is x:

x (3x-4)

For the second group, this is - 5:

-5 (3x-4)

The common factor for these two groups is (3x-4):

(3x-4) (x-5)