Infinite Algebra 2 - Test Review - Basic Operations of Polynomials

Advanced Algebra - Smith
Name___________________________________
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Test Review - Basic Operations of Polynomials
Date________________ Period____
1) When adding/subtracting/multiplying a polynomial with another polynomial, result is
always going to be ____________________________________.
2) Adding polynomials is as simple as combining ________________________________________.
3) Subtracting polynomials is just like adding, but first you must
____________________________________________ to the second polynomial.
4) To multiply polynomials, use the _______________________________________________.
5) The steps for dividing polynomials are:
1)________________________
2)________________________
3)________________________
4)________________________
5)________________________
Write each polynomial in standard form. Identify the degree and name each polynomial by
degree and number of terms.
6) p 2 + 8 p 5 - 8 p 4 - 9 p
7) 7n - 3n 4 - 4n 5 + 4n 2
8) 9 p 3 + 4 p 5 - 10 p 4 - 7 p 2 + 3
9) 10 - x - x 4 + 7 x 3
Worksheet by Kuta Software LLC
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Simplify each expression.
10) (8v 4 - 4 - 3v 2 ) + (7v 2 - 5 - 6v 4 )
11) (3 + 4k - 4k 2 ) - (2k 3 - 8 + 8k)
12) (8 x 2 - 4 x 3 - 3 x) - (4 x 2 + x 3 + 6 x) - (2 x 3 - 3 x)
13) 7(3a 2 - 6ab - b 2 )
14) (7 x + 3 y)( x + 5 y)
Worksheet by Kuta Software LLC
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15) (2 x - 3 y)(3 x 2 - 2 xy + 8 y 2 )
16) (4a 2 - 6ab + b 2 )(7a 2 + 8ab + 6b 2 )
Expand completely.
17) (2b + 3a) 3
18) (2 x - 3 y) 5
Find each coefficient described.
19) Coefficient of y 3 x 4 in expansion of ( y - 2 x) 7
20) Coefficient of n 4 m 2 in expansion of (2n + m) 6
21) Coefficient of xy 3 in expansion of (4 x + y) 4
Worksheet by Kuta Software LLC
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Divide.
22) ( x 4 + 13 x 3 + 35 x 2 - 12 x - 40) ¸ ( x + 4)
23) ( x 5 - 6 x 4 - 27 x 3 - 3 x - 17) ¸ ( x + 3)
24) (6 x 3 + 61 x 2 + 3 x - 63) ¸ (6 x + 7)
25) (7 p 4 + 54 p 3 + 77 p 2 + 58 p + 15) ¸ (7 p + 5)
Worksheet by Kuta Software LLC
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