Question

The area of a rectangle is given by 3x^3+14x^2-23x+6

Answer 1

The length of the rectangle is defined by $(x-1)\cdot \left(x-\frac{1}{3} \right)$.

Geometrically speaking, the rectangle area is equal to the product of its base and its length. According to the statement the area is represented by a third order polynomial and width by a first order polynomial and, thus, length must be a second order polynomial.

By factor the polynomial we get the following roots:

$A = 3\cdot x^{3}+14\cdot x^{2}-23\cdot x + 6$

$A = (x+6)\cdot (x-1)\cdot \left(x-\frac{1}{3} \right)$

Then, the length of the rectangle is defined by $(x-1)\cdot \left(x-\frac{1}{3} \right)$.

To learn more on rectangles, we kindly invite to check this verified question: brainly.com/question/10046743