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2 years ago

If a rectangle has an area of x^2+x-20 and a width of x-4, what is the length?

Mathematics

1 answer:

Mrac [35]2 years ago

4 0

Answer:

This (x - 5) represents the length of the rectangle.

Step-by-step explanation:

The formula for the area of a rectangle of length L and width W is A = L * W.

Here, the width is x - 4 and the area is x^2 + x - 20. Dividing the width (x - 4) into the area results in an expression for the length:

x - 4 / x^2 + x - 20

Let's use synthetic division here. It's a little faster than long division.

If the divisor in long division is x - 4, we know immediately that the divisor in synthetic division is 4:

4 / 1 1 -20

4 20

--------------------

1 5 0

This synthetic division results in a remainder of 0. This tells us that 4 (or the corresponding (x - 4) is indeed a root of the polynomial x^2 + x - 20, and so *(x - 4) is a factor. From the coefficients 1 and 5 we can construct the other factor: (x - 5). This (x - 5) represents the length of the rectangle.

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2 years ago

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