Answer:
[tex](5 x+ 3)(x + 4)[/tex]
Step-by-step explanation:
We want to factor
[tex]5 {x}^{2} + 23x + 12[/tex]
By comparing to
[tex]a {x}^{2} + bx + c[/tex]
We have a=5, b=23, c=12
ac=60
We split the middle term with 3x+20x, since 3×20=60
This implies that:
[tex]5 {x}^{2} + 3x + 20x + 12[/tex]
Factor by grouping;
[tex]x(5 x+ 3)+ 4(5x + 3)[/tex]
We collect common factors again;
[tex](5 x+ 3)(x + 4)[/tex]
