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Algebra II Polynomials and Linear Factors Work:
Several popular models of carry on luggage have a length 10 inches greater than the depth. To
comply with airline regulations, the sum of the length, width, and depth may not exceed 40 inches.
So the volume of the carry on would be V = L*W*D agreed?
a) Would you agree L + W + D = 40? Solve this equation for W.
b) Let depth = x
then
length =
and width =
c) Now substitute all your expressions into the volume equation without multiplying out.
It should be all terms with x’s in them
V(x) =
d) What are the x-intercepts? And what do these mean in the context of the problem?
f) Use a table to graph this problem.
Relative max _______
Relative min________
g) What is a reasonable domain for this function and why? (domain is x values)
h) What is the maximum possible volume of a piece of luggage? What are the corresponding
dimensions of the luggage?
Depth:
Length:
Width:
Volume:
i) Suppose the airline raises the allowable sum of luggage dimensions to 45 inches. Find the
maximum possible volume and corresponding dimensions.
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2) A rectangular box is 2x + 3 unit inches long, 2x – 3 unit inches wide, and 3x unit inches high.
Express its volume as a polynomial V(x).
3) Write the function in FACTORED FORM. Tell me the zeros and their multiplicity.
P(x) = 3x3 -27x2 +24x
4) Write a polynomial that has factors of 0 w/ multiplicity of 2, -3 and 2.
Decide if x + 4 is a factor of
x2 +6x + 8
x3 +3x2 -6x -7
Using zero has a place holder for any missing term.
If V(x) = x3 -13x + 12 and the length is x + 4, find the other two dimension.
Synthetic division: Takes out all variables and just uses numbers.
Opposite on the outside/coefficients on inside.
Drop first term and start multiplying and adding.
Divide 3x3 – 4x2 +2x – 1 by x + 1
Is -4 a factor of P(x) = x4 -5x2 +4x +12?
Homework when done with this: pg. 324 # 1-21eoo, 23, 27-31odd