The polynomial p(x) is given by p(x)=x^3 - 5x^2 - 8x + 48. Given (x+3) is a factor of p(x), express p(x) as a product of 3 linear factors.

This answer is easiest explained using the whiteboard in the interview. The question is basically asking for algebraic long division, we know (x+3) is a factor and are tasked with finding the other 2. We can start by writing the problem in standard long division form with p(x) inside and (x+3) outside. We need to think what can be multiplied by (x+3) to get a term of the same order as x^3. The answer is x^2 which can be written on top. Multiplying x^2 by x+3 gives x^3+3x^2 which can be subtracted from p(x) to give -8x^2-8x+48. Now we need to find what can be multiplied by (x+3) to give -8x^2: the answer is -8x. The multiplication gives -8x^2-24x which can also be subtracted to give 16x+48 (being careful with the double negatives). Finally, we need to find something that multiplies to give 16x+48: the answer is 16. Multiplying this and subtracting gives 0 which means we have found the factors of p(x). However, we are left with (x+3)(x^2-8x+16) which is not 3 factors. The second bracket can be factorized simply to give (x+3)(x-4)(x-4).