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Which polynomial represents the area of the rectangle?

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!! Which polynomial represents the area of the rectangle? class=

Answer :

Formula for Area:

[tex]A=lw[/tex]

We take the length and multiply it by the width:

[tex](3x-5)(x+1)[/tex]

We then need to foil. Multiply everything in the left expression by the right expression.

[tex]3x^2+3x-5x-5[/tex]

Combine like terms:

[tex]3x^2-2x-5[/tex]

Your answer would be:

B

highwireact

Let's start by looking at a rectangle with length 3x and width x + 1. I've broken the width into two chunks - the x chunk and the 1 chunk. If we look at the area of the two smaller rectangles, we can see that their areas are 3xx = 3x² and 3x(1) = 3x, making the total area so far 3x² + 3x. (Picture 1)

Now, to turn this rectangle into the one in the problem, we need to subtract 5 from the length. This has the effect of subtracting two smaller rectangles with areas 5x and 5 (picture 2), making our total area now 3x² + 3x - 5x - 5 (picture 3). Simplifying our expression, we find that the area of the rectangle in the problem is 3x² - 2x - 5 (picture 4)

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