Question

How many factors in the expression 8(x + 4)(y + 4)(z to the second power + 4z + 7) have two terms?

Answer 1

Would it help to write the factors like this?

8
(x+4)
(y+4)
(z^2 + 4z + 7)

Now count.

Answer 2

does factor mean a number to multiply to get another number in this situation?

Answer 3

"factor" mean when you divide by it, there is nothing left as a remainder. It must be a factor of the entire expression.

4 is a factor of 8 because 8/4 = 2 with no remainder.
3 is not a factor of 8 because 8/3 = 2 plus that pesky remainder of 2.
(x+1) is a factor of (x^2 - 1) because (x^{2} - 1)/(x+1) = x-1 with no remainder.

In your case: x+4 is a factor of 8 (x+4) (y+4) (z^2 + 4z + 7), because 8 (x+4) (y+4) (z^2 + 4z + 7)/(x+4) = 8 (y+4) (z^2 + 4z + 7) with no remainder.

4z is NOT a factor of 8 (x+4) (y+4) (z^2 + 4z + 7)

Are you starting to see it?

Answer 4

i choose 2