The annual orange production (in thousand tons) in the...

The annual orange production (in thousand tons) in the United States for the period 20112016 can be approximated by the polynomial $87 x^2-1131 x+9048$, where $x$ is the number of years after 2011. (Source: Based on data from the National Agricultural Statistics Service and bloomberg.com) a. Find the approximate U.S. orange production in 2015. To do so, let $x=4$ and evaluate $87 x^2-1131 x+9048$ b. Find the approximate U.S. orange production in 2013. c. Factor out the GCF from the polynomial $87 x^2-1131 x+9048$ ( Figure can't copy )

The annual orange production (in thousand tons) in the United States for the period 20112016 can be approximated by the polynomial $87 x^2-1131 x+9048$, where $x$ is the number of years after 2011. (Source: Based on data from the National Agricultural Statistics Service and bloomberg.com)
a. Find the approximate U.S. orange production in 2015. To do so, let $x=4$ and evaluate $87 x^2-1131 x+9048$
b. Find the approximate U.S. orange production in 2013.
c. Factor out the GCF from the polynomial $87 x^2-1131 x+9048$
( Figure can't copy )

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Key Concepts

Polynomial Evaluation

This concept involves substituting a specific value for the variable in a polynomial expression and calculating the result. It is a common technique used to determine the output of a function at a particular point, such as predicting values in a modeled situation. In applied contexts, this method helps translate abstract mathematical models into concrete numerical predictions.

Polynomial Factoring

This is the process of rewriting a polynomial as a product of simpler polynomials or factors. Factoring can reveal important features of the polynomial, such as its zeros or roots, and typically simplifies algebraic manipulation. This technique is useful in solving equations, simplifying expressions, and understanding the inherent structure of the polynomial.

Greatest Common Factor (GCF)

The Greatest Common Factor of a polynomial is the highest common factor that divides all the terms without leaving a remainder. Factoring out the GCF is a crucial step in simplifying polynomial expressions and is typically the first step in the factoring process. This method helps in reducing the polynomial to a simpler form, making subsequent factoring or solving procedures more straightforward.

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