How do you write a polynomial in standard form that represents the area of the shaded region of a rectangle when on the outside there are (x+4) and (x+7) and the inside the larger rectangle has (x+2) and (x+5) ... the shaded region is in between those two rectangles.

Question

Mathematics

Izayah Bridges

Yesterday, 00:17

How do you write a polynomial in standard form that represents the area of the shaded region of a rectangle when on the outside there are (x+4) and (x+7) and the inside the larger rectangle has (x+2) and (x+5) ... the shaded region is in between those two rectangles.

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Answers (1)

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Kade · Answer 1

F (x) = (x + 7) (x + 4) - (x + 5) (x + 2) =

= (x² + 4 x + 7 x + 28) - (x² + 2 x + 5 x + 10) =

= (x² + 11 x + 28) - (x² + 7 x + 10) =

= x² + 11 x + 28 - x² - 7 x - 10 = 4 x + 18

Answer:

The area of the shaded region is 4 x + 18.