Answer:
1x + 5
Step-by-step 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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