SOLUTION: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coeffcient of x^3. The coeffcient of x is three times the coeffcient of x^2. The remaining coeffcient is 2
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-> SOLUTION: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coeffcient of x^3. The coeffcient of x is three times the coeffcient of x^2. The remaining coeffcient is 2
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Question 235917: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coeffcient of x^3. The coeffcient of x is three times the coeffcient of x^2. The remaining coeffcient is 2 more than the coeffcient of x^3. The sum of the coeffcients is -4. Find the polynomial. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! polynomial in x has degree 3. (ax^3 + bx^2 + cx + d)
Let coefficient of x^3 = a
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The coefficient of x^2 is 3 less than the coeffcient of x^3.
b = (a-3)
:
The coefficient of x is three times the coefficient of x^2.
c = 3b
we want everything in terms of a, 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
replace b, c, d
a + (a-3) + (3a-9) + (a+2) = -4
a + a + 3a + a - 3 - 9 + 2 = -4
6a - 10 = -4
6a = -4 + 10
6a = +6
a = 1
then
b = 1 - 3
b = -2
and
c = 3(-2)
c = -6
and
d = 1 + 2
d = 3
:
x^3 - 2x^2 - 6x + 3 is the polynomial
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;
Check solution
1 - 2 - 6 + 3 = -4
