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leena

Hi there!

[tex]\large\boxed{P = 4x^2 + 12x + 22}[/tex]

The perimeter of a rectangle is:

P = 2l + 2w

Thus, plug in the given length and width:

P = 2(2x² + 5x + 8) + 2(x + 3)

Distribute:

P = 2(2x²) + 2(5x) + 2(8) + 2(x) + 2(3)

Simplify:

P = 4x² + 10x + 16 + 2x + 6

Combine like terms:

P = 4x² + 12x + 22

Wallameg000

Answer:

[tex]4x^2+12x+22[/tex]

Step-by-step explanation:

The perimeter of a rectangle is equal to [tex]2l+2w[/tex] where l is the length and w is the width. So, this rectangle would be equal to [tex]2\left(x+3\right)+2\left(2x^2+5x+8\right)[/tex]. Then, to find the polynomial simplify the expression. To do this first distribute the two 2s. This equals [tex]2x+6+4x^2+10x+16[/tex]. Then, add like terms to finish simplifying. This gives you the final answer of [tex]4x^2+12x+22[/tex].

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