21x^2 + 46x + 24
For the x^2 part it should factor into 7x * 3x or 21x * x
Let's try 7x * 3x:
(7x ) (3x )
For the 24 part there are a bunch of possibilities: 1 * 24, 2 * 12, 3 * 8, 4 * 6
Let's try 3 * 8
(7x 3) (3x 8)
7*8 = 56, 3*3 = 9
Can't make 46 out of 56 and 9. . .
(7x 8) (3x 3)
7*3 = 21, 8*3 = 24
Can't make 46 out of 21 and 24. . .
Let's try 4 and 6
(7x 4) (3x 6)
7*6 = 42, 4*3 = 12
Can't make 46 out of 42 and 12
(7x 6) (3x 4)
7*4 = 28, 6*3 = 18
We can make 46 out of 28 and 18, so let's try this:
(7x + 6) (3x + 4)
Expand that out and we get. . .
21x^2 + 46x + 24
That matches our original problem, so:
The factors of 21x^2 + 46x + 24 are (7x+6) and (3x+4)