What is the volume of this prism in terms of x, Mathematics

The area of the base of a prism can be expressed as x2 + 4x + 1 and the height of the prism can be expressed as x - 3. What is the volume of this prism in terms of x?

Because the formula for the volume of a prism is V = Bh, where B is the field of the base and h is the height of the prism, V = (x - 3)(x2 + 4x + 1). Use the distributive property  to multiply the ?rst term of the binomial, x, through each term of the trinomial,  and then the second term of the binomial, -3, through each term of the trinomial: x(x2 +    4x +    1)     3(x2+     4x  + 1). Then distribute:  (x • x2) + (x • 4x) + (x • 1) - (3 • x2) - (3 • 4x) - (3 • 1). Simplify by multiplying inside each term: x3 + 4x2 + x - 3x2 - 12x - 3. Use the commutative property to arrange such as terms further to each other. Notice which 1x = x: x3 + 4x2 - 3x2 + x -12x - 3; combine like terms: x3 + x2 - 11x - 3.

 

Posted Date: 5/21/2013 2:23:41 AM | Location : United States







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