ANSWER
[tex]f(x)=(5x+4)(5x-6)[/tex]
EXPLANATION
We want to factor the polynomial:
[tex]f(x)=25x^2-10x-24[/tex]
To do this, we have to find two numbers whose product is -120 (25 times -24) and sum up to -10.
Therefore, we have:
[tex]f(x)=25x^2-30x+20x-24[/tex]
Now, factor the polynomial:
[tex]\begin{gathered} f(x)=5x(5x-6)+4(5x-6) \\ f(x)=(5x+4)(5x-6) \end{gathered}[/tex]
That is the factored polynomial.
