Question

a rectangular piece of cardboard that is 10 inches by 18 inches has squares of length \\(x\\) inches on a side cut from each corner. (assume that \\(0 < x < 5\\).) represent the remaining area in the form of a polynomial function \\(a(x)\\).

answer
\\(a(x) =\\)

Explanation:

Calculate the total initial area

Using the Polynomial Applications knowledge point

$$ A_{\text{total}} = 10 \times 18 = 180 $$

Determine the area of the cut corners

Using the Polynomial Applications knowledge point

$$ A_{\text{corners}} = 4 \times (x \times x) = 4x^2 $$

Express the remaining area

Using the Polynomial Subtraction knowledge point

$$ A(x) = A_{\text{total}} - A_{\text{corners}} = 180 - 4x^2 $$

Answer:

A rectangular piece of cardboard that is 10 inches by 18 inches has squares of length x inches on a side cut from each corner. (Assume that 0 < x < 5.) Represent the remaining area in the form of a polynomial function A(x).

\(A(x) =\) <blank>\(180 - 4x^2\)</blank>