Final answer:
The question involves understanding and working with a quadratic polynomial function P(x) = -2(x-3)(x-11) in Mathematics. The roots can be found at x = 3 and x = 11. To calculate specific values, one would substitute x in the expression and simplify.
Step-by-step explanation:
The formula P(x) = -2(x-3)(x-11) represents a quadratic polynomial function in Mathematics. When analyzing such expressions, we often look at properties such as roots, vertex, and axis of symmetry. The roots are found by setting the function equal to zero, in this case at x = 3 and x = 11. To expand and simplify this function, we apply the distributive property (also known as the FOIL method) to get P(x) in the form of ax² + bx + c.
Multiplying binomials follows the rule of adding exponents when the bases are the same, as shown in the power rule x¹¹ * x¹, resulting in x¹¹⁰ⁱ or x¹¹+(-¹), which simplifies to x¹⁰ = 1 due to any number (except zero) raised to the zero power being 1. Also, negative exponents indicate that the base is in the denominator, thus x⁻¹ = 1/x.
To solve the function P(x) for a specific value, we would substitute that value into the expression and perform the arithmetic operations. For example, P(2) would be calculated by substituting x with 2 in the function: P(2) = -2(2-3)(2-11), and simplifying accordingly.