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Find the number that we can place in the box, so that the resulting expression can be factored as the product of two linear factors.
$$3mn - 6m + 5n + \boxed{\phantom{00}}$$

Thank you! :D

Apr 19, 2020

#1
+2

Hi floccinaucini!

So, we can start by noticing the signs. All of the signs are positive except for the $$-6m$$. So, that means that $$m$$ is multiplied by a negative number.

What we know right now: $$(\text{_}m+\text{_})(\text{_}n-\text{_})$$. (The _ are to symbolize the numbers we don't know.)

Since we know that we have a $$5n$$ term, we know that 5 goes in the black space next to m. Now we have $$(\text{_}m+5)(\text{_}n-\text{_})$$.

We also have a $$3mn$$ term, so let's put the 3 next to m. Now we have $$(3m+5)(\text{_}n-\text{_})$$

We also have a $$6m$$ term, so we know that something multiplied by 3m = 6m. $$\frac{6m}{3m}=2$$. Now we have  $$(3m+5)(n-2)$$

Now, we have covered all the terms. So let's multiply the factors out to find out what $$\square$$ is!

3m*n=3mn

3m*-2=-6m

5*n=5n

5*-2=-10

So they multiply to $$3mn-6m+5n-10$$. And now we can clearly that $$\square = -10$$!

I hoped this helped you floccinaucini!

:)



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Apr 19, 2020