The volume of the rectangular prism is given. Find an expression for the missing dimension. The given volume is 3x^3+8x^2-45x-50. The given expressions are x+5 and x+1.

Question

How to find the missing expression from the volume?

Answer 1

So the procedure is the same as if the dimensions were numbers: i.e. volume is 30 and dimensions are 2,5 and x. Find x. You would divide 30 by 2 and 5 to find x.

Same as here:

Volume = 3x³+8x²-45x-50

Dimension 1 = x+5

Dimension 2 = x+1

Find Dimension 3.

There are a variety of ways to get to the answer but I'll just show two ways.

Way 1 Multiply and Divide:

(x+5)(x+1) = x²+5x+x+5 = x²+6x+5

(3x³+8x²-45x-50)/(x²+6x+5) => Long Division gives us: 3x-10

Way 2 Simplify and Divide:

(3x³+8x²-45x-50)/[(x+5)(x+1)]

(3x²-7x-10)(x+5)/[(x+5)(x+1)]

(3x-10)(x+1)/(x+1)

3x-10

Ans: 3x-10