SOLUTION: x^2 −y^2 + mx + 5y − 6 = (ax + by +c)(dx + ey + f). Determine the values for a, b, c, d, e, f, and m.

Algebra.Com
Question 1127489: x^2 −y^2 + mx + 5y − 6 = (ax + by +c)(dx + ey + f). Determine the values for a, b, c, d, e, f, and m.
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

...first multiply right side of equation


compare coefficients and you see that:

->only when and
->only when and
....since and
....eq.1
since there is no term on left side
...only if and or and or vice versa
I will go with and
then
....eq.1



so, your solutions are:










Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
She only gave one solution.  Also she made some illegal assumptions. There
are 8 altogether, although there are really only 4, because the two parentheses
on the right can be in reverse order.  That would be a, b and c trading places
with d, e and f, respectively. For instance, solutions 1 and 3 below are
essentially the same.  Here are all 8 possibilities (4 essentially): 

1.   x² - y² + x + 5y - 6 = (-x - y + 2)(-x + y - 3), in which
     a=-1, b=-1, c=2, d=-1, e=1, f=-3, m=1

2.   x² - y² - x + 5y - 6 = (-x - y + 3)(-x + y - 2), in which
     a=-1, b=-1, c=3, d=-1, e=1, f=-2, m=-1

3.   x² - y² + x + 5y - 6 = (-x + y - 3)(-x - y + 2), in which
     a=-1, b=1, c=-3, d=-1, e=-1, f=2, m=1

4.   x² - y² - x + 5y - 6 = (-x + y - 2)(-x - y + 3), in which
     a=-1, b=1, c=-2, d=-1, e=-1, f=3, m=-1

5.   x² - y² - x + 5y - 6 = (x - y + 2)(x + y - 3), in which
     a=1, b=-1, c=2, d=1, e=1, f=-3, m=-1

6.   x² - y² + x + 5y - 6 = (x - y + 3)(x + y - 2), in which
     a=1, b=-1, c=3, d=1, e=1, f=-2, m=1

7.   x² - y² - x + 5y - 6 = (x + y - 3)(x - y + 2), in which
     a=1, b=1, c=-3, d=1, e=-1, f=2, m=-1

8.   x² - y² + x + 5y - 6 = (x + y - 2)(x - y + 3), in which
     a=1, b=1, c=-2, d=1, e=-1, f=3, m=1

Edwin
RELATED QUESTIONS

Given the following dependent system of equations Ax + By =C Dx + Ey = F where... (answered by stanbon)
Given the following independent system of equations Ax + By = C Dx + Ey = F Where... (answered by fractalier)
Given the following independent system of equations Ax + By = C Dx + Ey = F where A, B, (answered by Fombitz)
Given the following independent system of equations Ax + By = C Dx + Ey =F where A, B, (answered by Fombitz)
For each of the following expressions, simplify by expanding any brackets and collecting... (answered by user_dude2008)
Ax +by =c and dx+ey=f pls make x and y the subject of the... (answered by Fombitz)
16. Check f (x) = x3 − x for symmetry with respect to the x-axis (f (x) = −f (answered by jim_thompson5910)
x 0 1 2 3 f(x) 1 2 5 10 The table above... (answered by ewatrrr)
Solve the equations for the solutions, x and y. (Put your answers in simplest form.)... (answered by stanbon)