SOLUTION: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coefficient of x^3. The coefficient of x is three times the coefficient of x^2. The remaining coefficient

Algebra ->  Exponents -> SOLUTION: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coefficient of x^3. The coefficient of x is three times the coefficient of x^2. The remaining coefficient       Log On


   

Question 267263: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coefficient of x^3. The coefficient of x is three times the coefficient of x^2. The remaining coefficient is 2 more than the coefficient of x^3. The sum of the coefficients is -4. Find the polynomial.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
We will try to get every variable in terms of a
:
A polynomial in x has degree 3.
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
Replace b with (a-3)
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 coefficients is -4. Find the polynomial.
a + b + c + d = -4
Substitute, solve for a
a + (a-3) + (3a-9) + (a+2) = -4
6a - 10 = -4
6a = -4 + 10
6a = 6
a = 1
then
b = 1 - 3
b = -2
and
c = 3(1) - 9
c = -6
:
d = 1 + 2
d = 3
:
x^3 - 2x^2 - 6x + 3; is the polynomial