Can someone help me understand what i am supposed to do here?

[Applz]

Find the largest value of n such that 3x² + nx + 72 can be factored as the product of two linear factors with integer coefficients

 

[Dr.Peterson]

Find the largest value of n such that 3x² + nx + 72 can be factored as the product of two linear factors with integer coefficients

For example, \(3x^2 + 30x + 72\) can be factored as the product of two linear factors with integer coefficients -- try it.

Now, think about the method you used for that (I don't know what method you use, so you'll have to tell me). For what other numbers in place of 30 could you successfully factor it? Try to find the largest. Once you get a feel for how middle coefficients that work are formed, this will be easy.

Give it some thought and tell me whatever you can about it, and we can help you use those ideas. Again, how to do it will depend on what you have learned, so I'll want to see how you do the factoring, and what other ideas you have.

 

[pka]

Find the largest value of n such that 3x² + nx + 72 can be factored as the product of two linear factors with integer coefficients

You are looking for an expression \((3x+ j)(x+ k)=0\), in which \(j~\&~k\) are integers and \(j\cdot k=72\) and \(h+k\) is maximal.