Find the largest value of $n$ such that $5x^2+nx+48$ can be factored as the product of two linear factors with integer coefficients.

Step-by-step explanation:

Given

Required

Determine the highest value of n

From the given equation, 5 is a prime number;

So, the factors of x² is 5x and x or -5x and -x

Since has all shades of positive terms, we'll make use of 5x and x

The factorized expression can then be:

Open the brackets

Equate this to the given expression

By direct comparison;

 ---- (1)

--- (2)

From (2) above, the possible values of a and b are:

Of all these values; the value of a and b that gives the highest value of n is;

So;

Substitute 1 for a and 48 for b in (2)

Hence, the largest value of n is 241