Help me with ploynomials!?

Question

Can you please work this problem out in steps. I will give thumbs up and chose best answer.

(m squared + 2m -3) - ( -5m +3m squared -6)

Also if you can factor this polynomial in steps I would greatly appreciate it

3xy + 7x + 6y +14

Please show steps. Thank you.

Answer 1

m^2 +2m -3 - (-5m +3m^2 -6) =
m^2 +2m -3 + 5m -3m^2 + 6 =
-2m^2 +7m +3.

(The above result can't be easily factored --- it would involve surds --- so I presume that you mean not "...factor this polynomial..." but rather "...factor the NEXT polynomial..." Please try to avoid such ambiguity.)

3xy + 7x + 6y +14: start with 3x or 3y; can only get 14 by 2x7.
The 7 has to end up multiplying the x (so 3 can't be associated with the x term). Thus, the only way you can satisfy this is with
(x + ?)(3y + 7), so it must be (x + 2)(3y + 7). Check it out: it fits. BINGO!

Try to use similar reasoning yourself, next time.

Good luck; live long and prosper.

Answer 2

(m^2 + 3m - 3) - (-5m + 3m^2 - 6)
m^2 + 3m - 3 + 5m - 3m^2 + 6
(1 - 3)m^2 + (3 + 5)m + (-3 + 6)
-2m^2 + 8m + 3

------------------------------

3xy + 7x + 6y + 14
(3xy + 7x) + (6y + 14)
x(3y + 7) + 2(3y + 7)
(x + 2)(3y + 7)