Question

a rectangle has sides measuring (4x + 5) units and (3x + 10) units.
part a: what is the simplified expression that represents the area of the rectangle? show your work to receive full credit. (6 points)
part b: what are the degree and classification (by number of terms) of the expression obtained in part a? (4 points)

Explanation:

Part A

Step1: Recall the area formula for a rectangle

The area \(A\) of a rectangle is given by \(A = l\times w\), where \(l=(4x + 5)\) and \(w=(3x + 10)\). So, \(A=(4x + 5)(3x + 10)\).

Step2: Use the distributive property (FOIL method)

$$
LATEXBLOCK0
$$

Step3: Combine like - terms

\(12x^{2}+(40x + 15x)+50=12x^{2}+55x + 50\)

Part B

Step1: Determine the degree of the polynomial

The degree of a polynomial \(ax^{n}+bx^{m}+\cdots\) is the highest power of \(x\). In the polynomial \(12x^{2}+55x + 50\), the highest power of \(x\) is \(n = 2\).

Step2: Classify the polynomial by the number of terms

A polynomial with three terms \(ax^{2}+bx + c\) (\(a
eq0\)) is called a trinomial. The polynomial \(12x^{2}+55x + 50\) has three terms.

Answer:

Part A

The simplified expression for the area of the rectangle is \(12x^{2}+55x + 50\).

Part B

The degree of the polynomial is \(2\), and it is a trinomial.