A rectangular picture measuring 5 in. by 7 in. is surrounding by a frame with uniform width x. Write a quadratic function in standard form to show the combined area of the picture and frame.

(4x² + 24x + 35) in²

Step-by-step explanation:

(5+2x)(7+2x)

35 + 14x + 10x + 4x²

4x² + 24x + 35

A(x) = 4x² + 24x + 35

Step-by-step explanation:

Let x represent the width of the rectangular frame.

The formula for determining the area of a rectangle is expressed as

Area = length × width

The measurement of the rectangular picture is 5 in. by 7 in.

If the width is 5 inches, then the combined width of the picture and frame is 5 + x + x = (5 + 2x) inches

The combined length would be

7 + x + x = (7 + 2x) inches

Therefore, a quadratic function in standard form to show the combined area of the picture and frame would be

(5 + 2x)(7 + 2x)

35 + 10x + 14x + 4x²

A(x) = 4x² + 24x + 35