What is the coefficient of x^2 when -5x^3 - 5x^2 - 7x + 1 is multiplied by -x^2 + 6x + 1 and the like terms are combined?
(-5x3 - 5x2 - 7x + 1)(-x2 + 6x + 1)
To find the coefficient of x2, we can just multiply the terms that would have x2.
(-5x2)(1) + (-7x)(6x) + (1)(-x2)
= -5x2 - 42x2 - x2
Which means your coefficient is -48, which is also your answer :)