Tips For Success

Some questions on tests ask you to use polynomials to represent perimeter, area, and volume. Read the sample question below. Then follow the tips to answer it.

TIP 1

Make sure you look at the figure and understand it. This figure is a rectangular prism. The expressions x + 1, x + 2, and x + 3 represent the lengths of its edges.

The figure below is a rectangular prism.

Which expression represents the volume of the prism?

1. x 3 + 6 x cubed , plus 6
2. x 2 + 2 x + 2 x squared , plus 2 x plus 2
3. x 3 + x 2 + 10 x + 6 x cubed , plus , x squared , plus 10 x plus 6
4. x 3 + 6 x 2 + 11 x + 6 x cubed , plus , 6 x squared , plus 11 x plus 6

TIP 2

Be sure to answer the question being asked. In this problem, you need to find the volume of the prism.

Think It Through

The volume of a rectangular prism is given by V = ℓ w h . v equals script l w h .  Substitute the edge lengths into the formula. Then simplify the product.

V = ℓ w h   = ( x + 1 ) ( x + 2 ) ( x + 3 )   = ( x 2 + 3 x + 2 ) ( x + 3 )   = x 3 + 6 x 2 + 11 x + 6 table with 4 rows and 2 columns , row1 column 1 , v , column 2 equals script l w h , row2 column 1 , , column 2 equals open x plus 1 close open x plus 2 close open x plus 3 close , row3 column 1 , , column 2 equals open , x squared , plus 3 x plus 2 close open x plus 3 close , row4 column 1 , , column 2 equals , x cubed , plus , 6 x squared , plus 11 x plus 6 , end table

The correct answer is D.