Question

a piece of cardboard that is 5 inches by 11 inches has squares of length \\(x\\) inches on a side cut from each corner. (assume that \\(0 < x < 2\\).) represent the area in the form of a polynomial function \\(a(x)\\).

Explanation:

Express the area of the original cardboard

Using the Geometric Polynomial Modeling knowledge point

$$ \text{Total Area} = 5 \times 11 = 55 $$

Express the area of the four cut-out corners

Using the Geometric Polynomial Modeling knowledge point

$$ \text{Area of one corner square} = x^2 $$

$$ \text{Total cut-out area} = 4x^2 $$

Formulate the remaining area function

Using the Polynomial Simplification knowledge point

$$ A(x) = 55 - 4x^2 $$

Answer:

A piece of cardboard that is 5 inches by 11 inches has squares of length \(x\) inches on a side cut from each corner. (Assume that \(0 < x < 2\).) Represent the remaining area in the form of a polynomial function \(A(x)\).

\(A(x) =\) <blank>\(55 - 4x^2\)</blank>