Find the largest value of n such that 3x^2 + nx + 72 can be factored as the product of two linear factors with integer coefficients.

n = 217

Step-by-step explanation:

The quadratic expression that we have to factorize is 3x² + nx + 72.

So, we have to find factors of (3 * 72) i. e. 216.

Now, we can write 216 as

(1 * 216), Hence, 1 + 216) = 217

(2 * 108), Hence, 2 + 108 = 110

(3 * 72), Hence, 3 + 72 = 75

(4 * 54), Hence, 4 + 54 = 58

So on.

Therefore, to factorize 3x² + nx + 72, the maximum value of n which can be put in place of n to factorize the expression is 217. (Answer)