10v²+49v+18=(5v+2)(2v+9).
Factors of 10 are 10×1, 2×5; factors of 18 are 18×1, 9×2, 6×3
(av+b)(cv+d)=acv²+(ad+bc)v+bd
a |
c |
b |
d |
ad |
bc |
ad+bc |
10 |
1 |
18 |
1 |
10 |
18 |
28 |
10 |
1 |
1 |
18 |
180 |
1 |
181 |
10 |
1 |
9 |
2 |
20 |
9 |
29 |
10 |
1 |
2 |
9 |
90 |
2 |
92 |
10 |
1 |
6 |
3 |
30 |
6 |
36 |
10 |
1 |
3 |
6 |
60 |
3 |
63 |
5 |
2 |
18 |
1 |
5 |
36 |
41 |
5 |
2 |
1 |
18 |
90 |
2 |
92 |
5 |
2 |
9 |
2 |
10 |
18 |
28 |
5 |
2 |
2 |
9 |
45 |
4 |
49 |
5 |
2 |
6 |
3 |
15 |
12 |
27 |
5 |
2 |
3 |
6 |
30 |
6 |
36 |
The table contained all possible integer factors. The one we want is in red because 49 is the middle coefficient.