Question

a rectangle has an area of x2+8x+15 square meters and a width of x+3 what expression represents the length of the rectangle

Answer 1

1x + 5

Explanation:

Since the area of a rectangle of width w and length l is A = l*w,

length = Area / Width.

Here, x^2 + 8x + 15

length of rectangle = ----------------------

x + 3

Use synthetic division to perform the above. The coefficients of the quadratic are a = 1, b = 8 and c = 15, and the divisor is -3 (from (x + 3).

-3 / 1 8 15

-3 -15

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

1 5 0

Since the remainer is zero (0), -3 is a root and 1x + 5 is a factor of the quadratic. This factor, representing the length of the rectangle, is 1x + 5.

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