What constant must we place in the blank below in order to be able to factor the resulting expression into the product of two linear factors:
2mn - 16m - 7n + ____
well, you have
2m(n-8) - 7n
So, if you want a common factor of n-8, you would need 56
That would give you
2m(n-8) - 7n + 56
= 2m(n-8) - 7(n-8)
= (2m-7)(n-8)
Read what I wrote. I guarantee that you will find the answer.
Is the answer 56?
Yes
RealllyyY?Y?Y?YY?Y
To factor the expression 2mn - 16m - 7n + ____, we need to find a constant that completes the expression and allows us to write it as a product of two linear factors.
To determine the constant, let's look for terms that have a common factor.
First, we can group the terms together:
(2mn - 16m) - (7n - ____)
Now, let's focus on the first group, which consists of 2mn and -16m. The common factor here is 2m:
2mn - 16m = 2m(n - 8)
We can rewrite the expression as:
2m(n - 8) - (7n - ____)
Now, let's consider the second group, which consists of 7n and the constant we are looking for. We need to find a factor of 7n that, when multiplied by 2m, results in -7n. The factor is -7:
-7n = 2m * -7
So, the constant that completes the expression is -14:
2m(n - 8) - (7n - 14)
Now we have the expression factored into the product of two linear factors:
2m(n - 8) - 7(n - 14)