SOLUTION: If {{{(x^2 + 3x + 6)(x^2 + ax + b) = x^4 + mx^2 + n}}} for integers a, b, m and n, what is the product of m and n?

Algebra.Com
Question 1030211: If
for integers a, b, m and n, what is the product of m and n?
Found 2 solutions by robertb, Edwin McCravy:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
after expansion. This is supposed to be equal to
By equating coefficients, we obtain...
==> a+3 = 0,
m = b+3a+6,
3b+6a = 0, or b+2a = 0 after reduction,
6b = n
==> a = -3,
b = 6,
m = 6 - 9 +6 = 3, and
n = 6*6 = 36
==> mn = 3*36 = .
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
If
for integers a, b, m and n, what is the product of m and n?
Since this true for all x,



then it's true when x=0



.  Substitute 6b for n



It's also true when x=1:









It's also true when x=-1:









Multiply through by -1:



It's also true when x=2:





Divide through by 2







Solve the system:





Then take the value for b, substitute it in 
to find n.  Take the value for m, multiply it by
the value you get for n and get mn.  You finish.

Edwin
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