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Module 7 Test Review: Polynomials

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Module 7 Test Review: Polynomials
Name _______________________________________ Date __________________ Class __________________
Module 7 Test Review: Polynomials
1. Does each expression equal
2x 6  3x 4  x when simplified?
________________________________________
A ( x 6  2x 4  x 2 )  (  x 6  5 x 4  x 2  x )
Yes
No
B (2x 6  2x 4  x 2 )  ( x 4  x 2  x )
Yes
No
C (3x  2x  x 2  x )  ( x 6  x 4  x 2 )
6
4
Yes
No
D (4x  x  x )  (2x 6  3x 4  x 2 )
6
Yes
2
No
For 2–3, add the polynomials.
2. ( x 7  3x 6  x 2  4)  (3x 7  x 4  3x 2  9)
_______________________________________
3. (11x 9  3x 3 )  ( x 3  x )  (3x 9  x 6  8x )
_______________________________________
4. A rectangle has a width of x and a length
of 3x 3  5x  7. Does each expression
represent the perimeter of the rectangle?
A 2(3x 3  6x  7)
No
Yes
B 2(3x 3  4x  7)
No
Yes
C 6x 3  8x  14
No
Yes
D 6x 3  12x  14
No
Yes
5. Subtract the polynomials.
( 7 x10  2x 6  3 x 3 )  ( 2 x10  x 6  x 3  2)
 (3 x10  4 x 6  5 x 4  x 3  8)
_______________________________________
6. A rectangular swimming pool has a
perimeter of ( x 3  23x 2  17x  2) feet
and a width of x feet. Find the length of
the pool when the width is 24 feet.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
39
Name _______________________________________ Date __________________ Class __________________
7. Does each product result in x 4  y 4 ?
A ( x 2  y 2 )( x 2  y 2 )
Yes
No
B ( x 2  y 2 )( x 2  y 2 )
Yes
No
C ( x  y )( x  y )( x 2  y 2 )
Yes
No
D ( x  y )( x  y )( x 2  y 2 )
Yes
No
For 8–10, multiply the polynomials.
8. (2x  3)( x 2  4x  2)
_______________________________________
9. ( x 2  5x  3)(2x 3  3x 2  1)
_______________________________________
10. (3x  y )(9x 2  3xy  y 2 )
________________________________
11. The radius of a cylinder is x  2 and its
height is x 2  3x  2 . Find a function for
the volume of the cylinder.
_______________________________________
12. Choose True or False for each statement
about factoring 4x 2 y  16y .
A You can factor out the greatest
monomial factor.
True
False
B You can factor by grouping.
True
False
C You can factor using a perfect square
trinomial pattern.
True
False
D You can factor using the difference of
two squares pattern.
True
False
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
40
Name _______________________________________ Date __________________ Class __________________
Module 7 Test Review: Polynomials Module Quiz: B
D x  5
No
13. Is each polynomial irreducible?
A
x 4
No
Yes
B
x  12
No
Yes
C
x 2  10x  11
No
Yes
D
x 2  8x  12
No
Yes
6
3
E 8x 3  9
No
E
x
1
3
Yes
Yes
No
Yes
For 14–19, factor the polynomial, or
identify it as irreducible.
14. 9x 2  42x  49
_______________________________________
15. 15x 5  20x 4  6x 3  8x 2
_______________________________________
16. x 6  y 6
_______________________________________
17. 4x 3  27
_______________________________________
18. 3x 3  9x 2  12x  36
_______________________________________
19. 6x 5  54x
_______________________________________
20. Can synthetic division be used with each
of the following divisors?
x  10
No
Yes
B 2x  1
No
Yes
x2  2
No
Yes
A
C
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
41
Name _______________________________________ Date __________________ Class __________________
21. Use synthetic substitution to find p( 2)
and p( 1) for p( x )  x 4  4x 3  16x  16.
_______________________________________
22. Choose True or False for each statement
about the synthetic division shown below.
2
3 10 10 4
6 8 4
3
4
2
0
A One factor of (3x 3  10x 2  10x  4)
is ( x  2) .
True
False
B One factor of (3x 3  10x 2  10x  4)
is ( x  2) .
True
False
C One factor of (3x 3  10x 2  10x  4)
is (3x 2  4x  2) .
True
False
D One factor of (3x 3  10x 2  10x  4)
is (3x 3  4x 2  2x ) .
True
False
23. Use long division to find the quotient and
remainder. Write the result as
dividend  (divisor)(quotient)  remainder.
( x 4  3x 3  x 2  5x  3)  ( x 2  1)
_______________________________________
_______________________________________
24. Use synthetic division to find the quotient
and remainder. Write the result as
dividend  (divisor)(quotient)  remainder.
( x 3  5x 2  5x  2)  ( x  1)
_______________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
42
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