CCGPS Advanced Algebra WS: Extra Practice with Polynomials
1.
The volume of the rectangular prism is given by the equation
V(x) = 2x3 + 11x2 – 41 x – 140. Find the remaining factors of the
polynomial.
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2.
A carpenter hollowed out the interior of a block of wood as shown
at right.
A. Express the volume of the original block and the volume of the
wood removed as polynomials in standard form.
B.
Write a polynomial for the volume of the wood remaining.
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3. Since 2006, the water level in a certain lake can be modeled by the
polynomial d(x) = -x3 + 16x2 – 74x + 140. Where the depth, d, is
measured in feet over x years.
A. How many x-intercepts does the graph have? ____________
B. What are the coordinates have the x-intercept? ___________
C. In the context of the problem, what does the x-intercept
represent?
D. Identify the year that the pond will dry up. _________
E. Use the zero of the function to factor d(x), then identify the
quadratic equation represented by the depressed row. Solve.
F.
Classify the solutions of this quadratic equation. Make a conjecture about which types of solutions
occur as x-intercepts on the graph.
4. Suppose a polynomial has roots -2 + 5i,-i,and 1 + 6 . Find all of the roots and then state the least
possible degree of the polynomial.
5. Suppose a polynomial has roots -4, 2 and 3i . Find all the roots and then state the least possible
degree of the polynomial.
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6. Find the roots of each polynomial and state their multiplicities.
A. P(x) = (x + 3)2(x + 1)
B. P(x) = -8x4(x – 3)2(x + 4)3
C. P(x) = (x2 – 5x + 6)2
D. P(x) = (2x + 3)(4x – 5)(6x -7)(8x + 9)
E. P(x) = -4(x - 2) (x + π)5
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Find the all the zeroes of the function.
7. f(x) = 16x3 + 66x2 – 67x + 15 given that (2x - 1) is a factor.
8.
5
4
2
3
f(x) = 6x4 – 37x3 – 69x2 + 198x + 280 given f( )  0 and f( )  0