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?

Tutors, please sign in to answer this question.

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)

3m^2 +3mn + 7m +14m:

Just look at the common factor between terms

3 m^2 + 3mn + 7m +14n

greatest common factor between 1st and 2nd/ also between 3rd & 4th is 3m, therefore

3m(m +n) +7 ( m+n)

now (m+n) is GCF between 2 terms:

(m+n)(3m+7)

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