Chapter P, Prerequisites - Section P.5 - Algebraic Expressions - P.5 Exercises - Page 36: 89

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$V=x(6-2x)(10-2x)$ a. -Volume of a rectangular box is height times width times length. before it's unfolded, the width of the cardboard is $(10-2x)$ as shown by a broken line and the length is $(6-2x)$ as shown by a broken line. The height of the open box formed after folding at broken line is $x$. Therefore, by multiplying height times width times length can we get the expression for $V$. b. $V=x(6-2x)(10-2x)$ $V=4x^3-32x^2+60x,$ Polynomial of degree 3. c. $V=x(6-2x)(10-2x), x=1$ $V=64-31=32$ $V=x(6-2x)(10-2x), x=2$ $V=152-128=24$