The volume v (in cubic feet) of an aquarium is modeled by the polynomial function
v(x)=x3+2x2−13x+10
where x is the length of the tank.

a. explain how you know x = 4 is not a possible rational zero.
b. show that x - 1 is a factor of v(x). then factor v(x) completely.
c. find the dimensions of the aquarium shown.

Step-by-step explanation:

Using Synthetic division we have the coefficients

                                                             1            2         -13          10

dividing it by -4 we get                        ↓           -4         8            20

                                                             1            -2          -5           30

a. as 30 is the remainder so x-4=0 or x=4 is not a possible ratio

b.     for x-1 to be factor we divide it by x=1

                                                              1            2         -13          10

dividing it by 1  we get                        ↓             1            3           -10

                                                             1              3          -10           0

we get zero as the remainder . this shows that x-1 is a factor .

Solution: (x² +3x- 10)(x-1)

c.  Volume = L*B*H

V=  (x² +3x- 10) (x-1)

V= (x² +5x-2x-10)(x-1)

V= (x(x+5) -2(x+5))(x-1)

V= (x-2)(x+5)(x-1)

L*B*H=(x-2)(x+5)(x-1)

L= 2,B= 1, H=5 feet (-) sign indicates opposite direction