SOLUTION: The 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 3 times the coefficient of x^2. The remaining coefficient is

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The 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 3 times the coefficient of x^2. The remaining coefficient is      Log On


   

Question 156079This question is from textbook Prentice Hall Algebra 1
: The 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 3 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. This question is from textbook Prentice Hall Algebra 1

Answer by oscargut(2103) About Me  (Show Source):
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let P%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd
The coefficient of x^2 is 3 less than the coefficient of x^3.
then b=a-3
The coefficient of x is 3 times the coefficient of x^2.
then c=3b
The remaining coefficient is 2 more than the coefficient of x^3.
d=a%2B2
The sum of the coefficients is -4.
then
a%2Bb%2Bc%2Bd=-4
using
b=a-3
c=3b=3%28a-3%29=3a-9
d=a%2B2
sum is:
a%2B%28a-3%29%2B%283a-9%29%2Ba%2B2=-4
6a-10=-4
6a=6
a=1
then
b=a-3=1-3=-2
c=3a-9=3-9=-6
d=a%2B2=1%2B2=3
Answer:P%28x%29=x%5E3-2x%5E2-6x%2B3