Polynomial equation

Question

Atmospheric carbon dioxide levels continue to increase and are suspected to contribute to global warming. The solution to the polynomial equation:

x³-380x²+2x-760=0

gives the record high amount of carbon dioxide in parts per million (ppm) in 2005, as measured at Mauna Loa Observatory. Determine this record amount by:

1) Factoring the polynomial (pay attention to how many terms there are to determine how to factor)

2) Solving by setting each factor equal to zero.

 

3) Evaluating your results to see if they make sense in the context of the question. If a solution doesn't make sense, explain why not.

 

4) Writing a sentence that gives the labeled solution.

Answer 1

1)

 

Look at the polynomial to determine if you can factor by grouping, using FOIL, or using a binomial multiplied by a trinomial.  Notice that 2, 380, and 760 are multiples of 2.  We can try factor by grouping.

 

x²(x - 380) + 2(x - 380) = 0

 

 

The common factor on the left side of equation is (x - 380).

 

(x - 380)(x² + 2) = 0

 

 

2)

 

Set the factors equal to zero.

 

x - 380 = 0             and               x² + 2 = 0

 

 

3)

 

When you solve for x from the last step, your solutions should be real numbers.  Therefore, the last equation will not make any sense because when you solve for x, the solution is not real.

 

x² = -2

 

x = ±√(-2)

 

 

The square-root of a negative number is not a real value.

 

 

I will let you answer the last part on your own.