Question 47631
4x^3+35x^2+84x+45
The answer in the back of the book for that question was (4x+3)(x+3)(x+5) 

If that is the answer in the back of the book the algebraic expression 
is 4x^3=35x^2+24x+45 and not what you posted.

Now, how do you go about factoring it?

That depends on what you have learned up to this point in you study
of algebra.

1st You might graph it if you have a graphing calculator.
2nd You might know that if "p/q" is a zero of the expression 
   then p is a factor of 45 and q is a factor of 4.  Then if
   p/q is a zero one of the factors of the expression is (qx-p).

If you know these things you should be able to factor expressions
of this kind that have rational zeroes.

Cheers,
Stan H.