Answer:
[tex]n=241[/tex]
Step-by-step explanation:
We are given
[tex]5x^2+nx+48[/tex]
Let's assume it can be factored as
[tex]5x^2+nx+48=(5x-s)(x-r)[/tex]
now, we can multiply right side
and then we can compare it
[tex]5x^2+nx+48=5x^2-5rx-sx+rs[/tex]
[tex]5x^2+nx+48=5x^2-(5r+s)x+rs[/tex]
now, we can compare coefficients
[tex]rs=48[/tex]
[tex]5r+s=-n[/tex]
[tex]n=-(5r+s)[/tex]
now, we can find all possible factors of 48
and then we can assume possible prime factors of 48
[tex]48=-+(1\times 48)[/tex]
[tex]48=-+(2\times 24)[/tex]
[tex]48=-+(3\times 16)[/tex]
[tex]48=-+(4\times 12)[/tex]
[tex]48=-+(6\times 8)[/tex]
Since, we have to find the largest value of n
So, we will get consider larger value of r because of 5r
and because n is negative of 5r+s
so, we will both n and r as negative
So, we can assume
r=-48 and s=-1
so, we get
[tex]n=-(5\times -48-1)[/tex]
[tex]n=241[/tex]
