Question

Factor 2n^2 - 16n - 185x^2 + 45x + 100.

a) (2n - 20)(n + 9)
b) (2n + 20)(n - 9)
c) (2n - 5)(n + 10)
d) (2n + 5)(n - 10)

Answer 1

To factor the expression 2n^2 - 16n - 185x^2 + 45x + 100, you can group terms and factor them separately to find the factored form, which is (2n - 5)(n - 8).

Step-by-step explanation:

To factor the expression 2n^2 - 16n - 185x^2 + 45x + 100, we need to find two binomials whose product is equal to the given expression. We can do this by grouping terms and factoring them separately.

First, we group the terms as follows:

2n^2 - 16n - 185x^2 + 45x + 100 = (2n^2 - 16n) - (185x^2 - 45x) + 100

Then, we factor out the common factors from each group:

2n(n - 8) - 5x(37x - 9) + 100

Finally, we factor out any common factors from the resulting expression:

2(n - 8)(n) - 5(37x - 9)(x) + 100

Therefore, the factored form of the expression 2n^2 - 16n - 185x^2 + 45x + 100 is (2n - 5)(n - 8).