6.1 Review Worksheet, Part 1
6.1.1 Polynomials Identify the degree of each monomial. 1. x 8 2. 6 x 3 y
3. 8
4. a 4 b 6 c 3
Rewrite each polynomial in standard form. Then identify the leading coefficient, degree, and number of terms. Name the polynomial. 5. 3 x 3 + 2 x 4 − 7 x + x 2 6. 6 x − 4 x 4 + 5 7
7. 2 x 3 + 10 x − 9
8. 3 x 2 + 2 x 6 − 4 x 4 − 1
9. The distance d , in centimeters, that a diving board bends below its resting position when you stand at its end is dependent on your distance x , in meters, from the stabilized point. This relationship can be modeled by the function d ( x ) = − 4 x 3 + x 2 . a. Evaluate d ( x ) for x = 1 and x = 2.
b. Describe what the values d (1) and d (2) represent.
6.1.2 Adding and Subtracting Polynomials Add or subtract. Write your answer in standard form. 10. (15 x 2 − 3 x + 11) + (2 x 3 − x 2 + 6 x + 1)
11. (12 x − 1 + 2 x 2 ) + ( x 2 + 4)
12. (3 x 2 − 5 x ) − ( − 4 + x 2 + x )
13. ( x 2 − 3 x + 7) − (6 x 2 + 4 x + 12)
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