Question

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.

Answer 1

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

Answer 2

Explanation: