Question 125808
 The problem reads: "A polynomial in x has degree 3." Write it:
ax^3 + bx^2 + cx + d
: 
The coefficient of x^2 is 3 less than the coefficient of x^3.
b = a - 3
:
 The coefficient of x is three times the coefficient of x^2.
c = 3b
also, substituting (a-3) for b
c = 3(a-3)
c = 3a - 9
:
The remaining coefficient is 2 more than the coefficient of x^3.
d = a + 2
:
 The sum of the coefficient is -4. 
a + b + c + d =-4
:
Using the 1st 3 equations, substitute for b, c, d:
a + (a-3) + (3a-9) + (a+2) = -4
a + a - 3 + 3a - 9 + a + 2 = -4
we gather together:
a + a + 3a + a - 3 - 9 + 2 = - 4
6a - 10 = -4
6a = -4 + 10
6a = 6
a = 1
Then using the 1st 3 equations, substituting 1 for a
b = 1 - 3
b = -2
and
c = 3(1) - 9
c = -6
and
d = 1 + 2
d = 3
:
Find the polynomial.
:
y = x^2 - 2x^2 - 6x + 3