6.1 Review Worksheet, Part 1 (continued)
Add or subtract. Write your answer in standard form. 14. ( x 2 − 3 x + 4) + ( x 3 + 3 x − 4)
15. ( x 2 − 3 x + 4) − (3 x + x 3 − 4)
16. (5 y 3 − 2 y 2 − 1) − ( y 2 − 2 y − 3)
17. (2 y 2 − 5 y + 3) + ( y 2 − 2 y − 5)
6.1.3 Multiplying Polynomials Find each product. 18. 7 x 3 (2 x + 3)
19. 3 x 2 (2 x 2 + 9 x − 6)
20. xy 2 ( x 2 + 3 xy + 9)
21. 2 r 2 (6 r 3 + 14 r 2 − 30 r + 14)
22. ( x − y )( x 2 − xy + y 2 )
23. (2 x + 5 y )(3 x 2 − 4 xy + 2 y 2 )
24. ( x 3 + x 2 + 1)( x 2 − x − 5)
25. (4 x 2 + 3 x + 2)(3 x 2 + 2 x − 1)
26. A bottom for a box can be made by cutting congruent squares from each of the four corners of a piece of cardboard. The volume of a box made from an 8.5-by-11-inch piece of cardboard would be represented by V ( x ) = x (11 − 2 x )(8.5 − 2 x ), where x is the side length of one square. a. Express the volume as a sum of monomials.
X
Jill ’s FLOWERS
8.5 in.
X
11 in.
b. Find the volume when x = 1 inch.
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