Question 1045163
How do I solve this word problem?
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.
<pre> You only need ONE (1) variable. Don't confuse yourself with too many unnecessary variables.
Let the coefficient on {{{x^3}}} be a
Then the coefficient on {{{x^2}}} = a - 3
The coefficient on x is: 3(a - 3)
The constant is: a + 2
This gives us: {{{matrix(4,1, ax^3,(a - 3)x^2,3(a - 3)x,(a + 2))}}}
Since all coefficients sum to  - 4, we get: a + (a - 3) + 3(a - 3) + (a + 2) = - 4
a + a - 3 + 3a - 9 + a + 2 = - 4
6a - 10 = - 4
6a = 6
a = 1
Therefore, {{{matrix(4,1, ax^3,(a - 3)x^2,3(a - 3)x,(a + 2))}}} becomes: {{{matrix(4,1, 1x^3,(1 - 3)x^2,3(1 - 3)x,(1 + 2))}}} ----- Substituting 1 for a
The polynomial is: {{{highlight_green(x^3 - 2x^2 - 6x + 3)}}}
It is that simple...nothing COMPLEX!