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2:11
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A-SSE.2 -- Recognize and rewrite expressions using Diff 2 squares, binomial squared, Sum/Difference of Cubes
A-APR.3 -- Find zeroes of higher-order polynomial functions graphically and from factors, (cubic and quartic.)
A. Read the information, write a function in factored form and then answer the questions.
1. A rectangular box has a
square base. The combined
length of a side of the square
base, and the height is 10 in. Let
x be the length of a side of the
base of the box.
What is the maximum possible
volume of the box?
4. The volume V of a container
is 84 ft3. The width, the length,
and the height are x, x + 1, and
x  4 respectively. What are the
container’s dimensions?
2. The length of a box is 2 times
the height. The sum of the length,
width, and height of the box is 10
centimeters.
Find the maximum volume of the
box and the dimensions of the box
that generates this volume.
3. A jewelry store is designing a
5. The product of three
consecutives integers is 336.
What are the integers?
6. Your brother is 3 years older
than you. Your sister is 4 years
younger than you.
The product of your ages is 1872.
How old is your sister?
gift box. The sum of the length,
width, and height is 12 inches. If
the length is one inch greater the
height, what should the dimensions
of the box be to maximize
its volume? What is the maximized
volume?
.
B. Find all of the zeros for the polynomials and polynomial functions
1. x5  3x4  8x3  8x2  9x  5 = 0
2. x4 + 3x3  21x2  48x + 80 = 0
3. x4 + 15x2  16 = 0
4. f(x) = x3  9x2 + 27x  27
5. y = x3  10x  12
6. f(x) = 2x3 + x  3
7. g(x) = x3 + 4x2 + 7x + 28
8. g(x) = x4  5x2  36
9. y = x4 + x3 7x2  9x 18
H. Use the remainder theorem to find the missing coefficient.
2. If f(x) = (2x4 + Mx2 + 4) has a
1. If (x 2) is a factor of
3
2
remainder of 20 when divided by
P(x) = x
Kx 7x 10
(x  2), find M
Find K.
3. If f(x) = x3 3x2 + x + K has
(x  3) as a factor, find K
C. Use factoring techniques to solve
1. 4x3  32 = 0
2. 27x3 + 1 = 0
3. 64x3  1 = 0
5. x4  9x2 + 14 = 0
7. x4  10x2 + 9 = 0
6. x4 + 13x2 + 36 = 0
4. x3  27 = 0
8. x4 + 3x2  4 = 0