help dividing polynomial by trinomial!! plz help!!?

Question

could someone plz explain step by step how to divide this polynomial by this trinomial??

m^2-9mn+14n^2  
------------------------       
m^2+7mn+12n^2                              

divided by

3m^2-21mn
----------------
4m^3+16m^2n

just in case - the ^ symbol means to the power of.. so 16m^2n is 16(m^2)(n) hopefully i typed the question out clearly enough.
and if it would b any comfort ill let u know, this isnt an actual question, im doing review for a test and i chose the questions i did, but i cant figure this one out. so i would appreciate it very much if someone would take the time to explain it step by step clearly.
thank u so much if u do!!

mohanrao d · Accepted Answer

m^2 - 9mn + 14n^2.....3m^2 - 21mn
_________________÷_____________
m^2 + 7mn + 12n^2.....4m^3+16m^2n

(m - 7n)(m - 2n).....3m(m - 7n)
______________÷_____________
(m + 4n)(m+3n)......4m^2(m + 4n)

(m - 7n)(m - 2n).....4m^2(m + 4n)
_____________x...___________
(m + 4n)(m+3n).....3m(m - 7n)

(m - 2n)....4m
_______x_____
(m+3n)........3

4m(m - 2n)
__________
3(m + 3n)

YadaYadaYada · Answer

I'll do each quadratic/cubic individually then put it all together at once.

a = m^2-9mn+14n^2 = (m - 7n)(m - 2n)
b = m^2+7mn+12n^2 = (m + 4n)(m + 3n)

c = 3m^2-21mn = 3m(m - 7n)
d = 4m^3+16m^2n = 4m^2(m + 4n)

Then you have

(a / b)  / (c / d) = ad / bc

     (m - 7n)(m - 2n)*4m^2(m + 4n)
= ------------------------------------------------
     (m + 4n)(m + 3n)*3m(m - 7n)

      4m^2(m-2n)
= ----------------------
      3m(m+3n)

      4m(m-2n)
= ----------------------
      3(m+3n)

cidyah · Answer

m^2-9mn+14n^2 
=m^2-7mn-2mn+14n^2
=m(m-7n)-2n(m-7n)
(m-7n)(m-2n)

m^2+7mn+12n^2 
=m^2+4mn+3mn+12n^2
=m(m+4n)+3n(m+4n)
(m+4n)(m+3n)

3m^2-21mn
=3m(m-7n)

4m^3+16m^2n
4m^2(m+4n)

Substitute these expressions in the above problem. Cancel like terms in the numerator and the denominator.
(m-7n)(m-2n) 4m^2(m+4n)
------------------------------------
(m+4n)(m+3n)3m(m-7n)

4m^2(m-2n) 
-------------------
3m(m+3n)

4m(m-2n)
----------------
3(m+3n)

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help dividing polynomial by trinomial!! plz help!!?

3 Answers