Answer:
The correct answer is: width b = x - 1
Step-by-step explanation:
Given:
Polynomial function or cubic equation which represents the volume of the rectangular prism P(x) = x³ + 9 x² + 6 x - 16
The formula to calculating volume of the rectangular prism is:
V = a · b · c Where a is length of the base, b width of the base and c is height
In this case a = x + 2, c = x + 8 and b = ?
We can factorize the given equation using the Bezu theorem :
P(1) = 1³ + 9· 1² + 6 · 1 - 16 = 0
This means that the polynomial is divided by the binomial (x - 1) without residue.
We will divide polynomial function with binomial (x - 1)
(x³ + 9 x² + 6 x - 16) : (x - 1) = x² + 10 x + 16
When we multiply a · c = (x + 2) (x + 8) = x² + 10 x + 16
We have formula V = a · b · c, from which we conclude that
width is b = (x - 1)
The second solution is to divide P(x) with a · c = (x + 2) (x + 8) = x² + 10 x + 16
and get b = (x - 1)
God with you!!!
