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 coefficie

Question 181077This question is from textbook
: 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. This question is from textbook

Answer by eperette(173) (Show Source): You can put this solution on YOUR website!
polynomial in x of degree three would look something like this:
ax^3 + bx^2 + cx + d
where a,b,c, and d are real numbers (coefficients)
given:
b= a-3
c= 3b = 3(a-3)
d= a+2
a+b+c+d= -4
solution:
a+(a-3)+3(a-3)+(a+2) = -4
a + a -3 +3a -9 + a + 2 = -4
6a -10 = -4
6a = 6
a =1
then
b= 1-3 = -2
c= 3b = 3(-2) = -6
d= a+2 = 1+2=3
so polynomial is:
1x^3 -2x^2 -6x +3 or x^3-2x^2-6x+3

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