Question

Please can someone help?

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear factors.

3mn - 6m + 5n +____

Answer 1

-10

Explanation:

First we need to factor the two first terms of the expression:

3mn - 6m = 3m * (n - 2)

Then, if we want to find in the end a product of two linear factors, we need the other two terms of the expression to have a common term of (n-2).

If the third term is 5n and the factors need to be linear, we can have 5 as the common factor:

5 * (n-2) = 5n - 10

So the fourth term is -10, then we would have:

3mn - 6m + 5n - 10

3m * (n - 2) + 5 * (n - 2)

(3m + 5) * (n - 2)