4. The total consumption of fossil fuels in the United States per year can be represented by the function C(x) = 0.0439x3 – 1.4911x2 + 14.224x + 41.76, where x is the number of years after 1970, and C(x) represents the amount of energy consumed in quadrillions of BTUs (or “quads”). In 1979, the U.S. consumed 81 quads of energy.
Subtract C(x) – 81 and write down the resulting function. Since you know that 9 is a root of this function, find the other two roots. In what year after 1979 did the U.S. consumption of energy also reach 81 quads?
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After you have calculated the C(x) - 81, you can proceed as follows:
The third-degree function can be written as (x - a)(x - b)(x- c) where a,b,c are the roots. Since we know 9 is a root, you can proceed with polynomial division by term (x - 9). The remainder function can be solved using the standard formula (or further algebraic manipulation)