express the area of the plane figure shown as a polynomial in standard form. the area of the figure…

express the area of the plane figure shown as a polynomial in standard form. the area of the figure expressed as a polynomial in standard form is (type an expression using x as the variable.)

express the area of the plane figure shown as a polynomial in standard form. the area of the figure expressed as a polynomial in standard form is (type an expression using x as the variable.)

Answer

Explanation:

Step1: Divide the figure into rectangles

We can divide the given figure into two rectangles. One rectangle has dimensions (x) by (x) and the other has dimensions (x - 3) by (x+5 - x=5).

Step2: Calculate the area of the first rectangle

The area of a rectangle is (A = l\times w). For the first rectangle with length (l = x) and width (w = x), the area (A_1=x\times x=x^{2}).

Step3: Calculate the area of the second rectangle

For the second rectangle with length (l = 5) and width (w=x - 3), the area (A_2=5\times(x - 3)=5x-15).

Step4: Find the total area

The total area (A) of the figure is the sum of the areas of the two rectangles, (A=A_1 + A_2=x^{2}+5x - 15).

Answer:

(x^{2}+5x - 15)