Asked by alexis
he dimensions of a rectangular prism are (5x squared - 4x - 3) (x squared - x + 1) cm by (3x squared - 5) cm. Find a polynomial which represents
1. the total surface are of the prism.
2. the total length of the edges of the rectangular prism
3. the volume of the prism.
1. the total surface are of the prism.
2. the total length of the edges of the rectangular prism
3. the volume of the prism.
Answers
Answered by
Damon
L=(5x^2-4x-3) w=(x^2-x+1) h=(3x^2-5)
use distributive property for multipication
Lw:
5 x^2(x^2-x+1) = 5x^4-5x^3+5x^2
-4x(x^2-x+1)= -4x^3+4x^2-4x
-3(x^2-x+1)= -3x^2 +3 x -3
add
Lw = 5 x^4 - 9 x^3 + 6 x^2 -x - 3
for side areas
2 Lw = 10x^4-18x^3+12x^2-2x-6
do the same for top and bottom and ends and add for area
use distributive property for multipication
Lw:
5 x^2(x^2-x+1) = 5x^4-5x^3+5x^2
-4x(x^2-x+1)= -4x^3+4x^2-4x
-3(x^2-x+1)= -3x^2 +3 x -3
add
Lw = 5 x^4 - 9 x^3 + 6 x^2 -x - 3
for side areas
2 Lw = 10x^4-18x^3+12x^2-2x-6
do the same for top and bottom and ends and add for area
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