Given:
[tex]2n^2+4n-48[/tex]
To factor the given expression, we first factor out the common term 2:
[tex]2n^2+4n-48=2(n^2+2n-24)[/tex]
Next, we note that -4 and 6 are the two numbers that add up to 2 and multiply -24. Hence, we rewrite the expression:
[tex]n^2+2n-24=(n-4)(n+6)[/tex]
Therefore, the answer is:
[tex]2(n-4)(n+6)[/tex]
