Question

Factor 3x^2-19x+20 ​

Answer 1

Answer:

(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)