# 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 ->  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

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 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(15746)   (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