SOLUTION: If anyone could help me with this problem, it would be greatly appreciated. The problem reads: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coeffici

Question 125808This question is from textbook Introductory Algebra
: If anyone could help me with this problem, it would be greatly appreciated. The problem reads: 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 coefficient is -4. Find the polynomial. This question is from textbook Introductory Algebra

Found 3 solutions by stanbon, ankor@dixie-net.com, MathLover1:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
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 coefficient is -4. Find the polynomial.
--------------------
Let the coefficients be a,b,c,d.
---------------------
EQUATIONS:
a + b + c + d = -4
a - b + 0 + 0 = 3
3a+ 0 - c + 0 = 9
a + 0 + 0 - e =-2
---------------------
Solved using TI Matrix function:
a = 1
b = -2
c = -6
d = 3
---------------------
polynomial
x^3-2x^2-6x+3
================
Cheers,
Stan H.
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
The problem reads: "A polynomial in x has degree 3." Write it:
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
also, substituting (a-3) for b
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 coefficient is -4.
a + b + c + d =-4
:
Using the 1st 3 equations, substitute for b, c, d:
a + (a-3) + (3a-9) + (a+2) = -4
a + a - 3 + 3a - 9 + a + 2 = -4
we gather together:
a + a + 3a + a - 3 - 9 + 2 = - 4
6a - 10 = -4
6a = -4 + 10
6a = 6
a = 1
Then using the 1st 3 equations, substituting 1 for a
b = 1 - 3
b = -2
and
c = 3(1) - 9
c = -6
and
d = 1 + 2
d = 3
:
Find the polynomial.
:
y = x^2 - 2x^2 - 6x + 3
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

A polynomial of degree :
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.

��.(2)
��..(3)
��(4)

��(1)..=>�.plug in (3)
��..(3)
�
��.(I)
��(4).substitute from (1), from (3), and from (I)

��solve for
��
��
��
��
Now find
��(1)

Now find
��.(2)

Now find
��.(I)
��
��
So, your coefficients are:

��

��

A polynomial of degree will be:

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