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Ques 8:
The Volume(V) in cubic feet of an aquarium id modeled by the polynomial function V(x)=
a) We have to explain that why x =4 is not a possible rational zero.
By Factor theorem, which states that a polynomial f(x) has a factor (x - k) if and only if f(k)=0.
For this , we will substitute the value of x in the given function.
which is not equal to zero.
Therefore, x=4 is not a possible rational zero.
(b) To show that (x-1) is a factor of V(x).
By Factor theorem, which states that a polynomial f(x) has a factor (x - k) if and only if f(k)=0.
Let (x-1)=0
So, x=1.
Substituting x=1 in the given function.
V(1) = 0
Therefore, (x-1) is a factor of V(x).
Now we will factorize the given function.
Dividing the given function by (x-1).
On dividing, we get quotient as
So, factored form is =
=
=
=
(c) So, the dimensions are 1,2 and -5.
Let's call x1: The rate per hour of the number one mechanic. X2: The rate per hour of mechanic number two. The first thing you should do is identify the system of equations that best describes the problem. In this case it is a system of 2 equations with two unknowns which when solved gives a total of x1 = 85 $ / h and x2 = 50 $ / h. Attached solution.
