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The football field is rectangular. The length of the rectangular football field is divided into 3 portions. The length of the first and third portion is x inches. The length of the second portion is 300 feet. The width of the football field is left-parenthesis 4 times x plus 40 right-parenthesis feet. a. Write a polynomial that represents the area of the football field.

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28jstinebaugh

Answer:

The area of a rectangle is expressed as;

A = l × w

where l is the length and w is the width

length = x + x + 300 = 2x + 300

breadth = 4x + 40

1. A = (4x + 40)( 2x + 300)

= 4x)( 2x + 300) + 40(2x + 300)

= 8x² + 1200x + 80x + 12000

= 8x² + 1280x + 1200

Therefore, the polynomial that represents the area of the football field is 8x² + 1280x + 1200.

Step-by-step explanation:

Thank u lholaboyeadedotun

msm555

Answer:

[tex] 8x^2 + 1280x + 12000 [/tex]

Step-by-step explanation:

To find the area of the football field, we need to multiply its length by its width. Let's denote:

  • Length of the first and third portions as [tex] x [/tex] inches each.
  • Length of the second portion as [tex] 300 [/tex] feet.
  • Width of the football field as [tex] (4x + 40) [/tex] feet.

The length of the football field is the sum of the lengths of the three portions, which is:

[tex] 2x + 300 [/tex] feet

The width of the football field is:

[tex] 4x + 40 [/tex] feet

So, the area [tex] A [/tex] of the football field is given by:

[tex] \sf Area(A) = \textsf{Length} \times \textsf{Width} [/tex]

[tex] \sf Area(A) = (2x + 300) \times (4x + 40) [/tex]

Expanding this expression, we get:

[tex] \sf Area(A) = 8x^2 + 80x + 1200x + 12000 [/tex]

[tex] \sf Area(A) = 8x^2 + 1280x + 12000 [/tex]

Therefore, the polynomial that represents the area of the football field is:

[tex] \Large\boxed{\boxed{8x^2 + 1280x + 12000 }}[/tex]

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