Answer:
[tex]a=3\text{ and } b=-17[/tex]
Step-by-step explanation:
We are given that:
[tex]5x^2+bx-12=(5x+a)(x-4)[/tex]
First, we can distribute the right-hand side:
[tex]5x(x-4)+a(x-4)[/tex]
Distribute:
[tex]=5x^2-20x+ax-4a[/tex]
Rewrite:
[tex]=5x^2+(-20+a)x-(4a)[/tex]
Since it is equivalent to the above expression, the coefficients of the variables must match. This means that:
[tex]-20+a=b\text{ and } 12=4a[/tex]
Solving for a in the second equation gives:
[tex]a=3[/tex]
Therefore:
[tex]b=-20+3=-17[/tex]
