SOLUTION: I was hoping you could provide me some direction as to how to solve this polynomial word problem. A polynomial in x has degree 3. The coefficient of x(with an exponent of 2) is

Question 141373This question is from textbook Introductory Algebra
: I was hoping you could provide me some direction as to how to solve this polynomial word problem.
A polynomial in x has degree 3. The coefficient of x(with an exponent of 2) is 3 less than the coefficient of x(with an exponent of 3). The coefficient of x is three times the coefficient of x(with an exponent of 2). The remaining coefficient is 2 more than the coefficient of x(with an exponent of 3). The sum of the coefficients is -4. Find the polynomial. This question is from textbook Introductory Algebra

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A polynomial in x has degree 3. The coefficient of x(with an exponent of 2) is 3 less than the coefficient of x(with an exponent of 3). The coefficient of x is three times the coefficient of x(with an exponent of 2). The remaining coefficient is 2 more than the coefficient of x(with an exponent of 3). The sum of the coefficients is -4. Find the polynomial.
:
Let a = coefficient of x^3
:
Write an expression for each statement:
;
"The coefficient of x^2 is 3 less than the coefficient of x^3"
(a-3)
:
"The coefficient of x is three times the coefficient of x^2."
3(a-3)
:
"The remaining coefficient is 2 more than the coefficient of x^3".
(a+2)
:
"The sum of the coefficients is -4."
a + (a-3) + 3(a-3) + (a+2) = -4
a + a - 3 + 3a - 9 + a + 2 = -4
6a - 10 = -4
6a = -4 + 10
6a = +6
a = +1
:
Using a = 1 we can write it:
(1)x^3 + (1-3)x^2 + 3(-2)x + (1+2)
:
y = x^3 - 2x^2 - 6x + 3; is the polynomial
:
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