Could I please just have a brief explanation?
Why are you not able to factor the polynomial: 7m + 6mn + 3m^2 + 14n by grouping?
Could I please just have a brief explanation?
Why are you not able to factor the polynomial: 7m + 6mn + 3m^2 + 14n by grouping?
This is factorable by grouping. One thing to consider is that terms are commutative, meaning they can be rearranged.
7m + 6mn + 3m^{2} + 14n
Rearrange terms and group 1st two and 2nd two==> (7m + 14n) + (6mn + 3m^{2})
From each group, factor out the GCF ==> 7(m + 2n) + 3m(2n + m)
Notice that the quantities in bold are identical (this let's you know you did the technique correctly). So now, the GCF of this new expression is the quantity (2n + m), so let's factor that out.
(2n + m)(7 + 3m) ==> note that if you distribute the bold quantity, you'd get the above expression again.
It looks like you can:
3m^{2} + 6mn + 7m + 14n
3m(m + 2n) + 7(m + 2n)
(3m + 7)(m + 2n)