Question

the polynomial - 17x^2+187x + 14,403 represents the electricity generated (in gigawatts) by geothermal sources during 2002 - 2007. the polynomial 88x^2-71x + 10,185 represents the electricity generated (in gigawatts) by wind power during 2002 - 2007. in both polynomials, x represents the number of years after 2002. find a polynomial for the total electricity generated by both geothermal and wind power during 2002 - 2007. the polynomial for the total electricity generated is (type your answer using exponential notation.)

Explanation:

Step1: Identify the polynomials

The polynomial for electricity generated by geothermal sources is $88x^{2}-71x + 10185$ and by wind - power is $-17x^{2}+187x + 14403$.

Step2: Add the polynomials

To find the total electricity generated by both sources, we add the two polynomials:
\[

$$\begin{align*} &(88x^{2}-71x + 10185)+(-17x^{2}+187x + 14403)\\ =&(88x^{2}-17x^{2})+(-71x + 187x)+(10185 + 14403)\\ =&71x^{2}+116x+24588 \end{align*}$$

\]

Answer:

$71x^{2}+116x + 24588$