How do you factor 3m2 plus 32m plus 64 and please explain?

Answer 1

It's not very scientific, but I usually solve these things with a mixture of common sense and trial and error. Call it educated guessing.

The 3 in 3m2 only has two factors, so your brackets will start out with 3m and m.

(3m )(m )

All of the operational signs are pluses. The brackets will have them too.

(3m + )(m + )

Now you're looking for factors of 64 that will solve the equation. 64 only has four factor pairs, so it won't take long to try them all. 64 and 1 won't work. 32 and 2 won't work. 16 and 4 won't work.

(3m + 8)(m + 8)

Check it using the FOIL method. (First, Outside, Inside, Last)

3m x m = 3m2

3m x 8 = 24m

8 x m = 8m

(24m + 8m = 32m)

8 x 8 = 64

(3m + 8)(m + 8) = 3m2 + 32m + 64.

It checks.