Question

F(x)=4x^(2)-6 Simplify your answer as much as possible

Answer 1

The final simplified form of the given function
`\(F(x) = 4x^2 - 6\) is \(F(x) = 2(2x^2 - 3)\)`, where the common factor of 2 has been factored out.

Step-by-step explanation:

The given function is
`\(F(x) = 4x^2 - 6\)`. To simplify, we can factor out the common factor from the terms. In this case, the common factor is 2. Factoring out 2, we get:

`\[F(x) = 2(2x^2 - 3)\]`

Now, the expression
`\(2x^2 - 3\`) cannot be further factored since it is a quadratic expression with no common factors. Therefore, the simplified form of
`\(F(x)\) is \(2(2x^2 - 3)\)`.

In summary, the simplified form of the given function
`\(F(x) = 4x^2 - 6\) is \(2(2x^2 - 3)\)`, where the common factor 2 has been factored out. This form is more concise and easier to work with, providing a clearer representation of the original function.

This simplification process is essential in mathematics for various reasons, including making expressions more manageable, identifying key features of functions, and facilitating further analysis or computations. It allows mathematicians and scientists to express complex relationships in a more concise and understandable manner, aiding in the interpretation and application of mathematical models.