Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?

Factoring by grouping usually pairs up the first 2 sets of expressions with the second 2 sets.  Ours looks like this, then:  .  If we factor out the common x-squared in the first set of parenthesis, along with factoring out the common 5 in the second set, we get this:  .  Now the common expression that can be factored out is the (x-9).  When we do that, here's what it looks like:  .  I'm not sure how far you are going with this.  You could set each of those equal to 0 and solve for x in each case.  The first one is easy.  If x - 9 = 0, then x = 9.  The second one involves the imaginary i since x^2 = -5.  In that case,  .  Hopefully, in what I have given you, you can find what you're looking for.

For the first question the answer is a, for the second c, for the third d, for the 4th b, for the 5th a

Ithink you answer is c