# I. State the degree and leading coefficient of each polynomial in one

## Transcription

I. State the degree and leading coefficient of each polynomial in one

1 Polynomial Worksheet I. State the degree and leading coefficient of each polynomial in one variable. If it is not a polynomial in one variable, explain why. 1. 3 +6 4. (3 7. 4 – – 9) + 1)(2 +6 – +7 + 20 + 10 –9 5. 8 – 10 +8 10. 18 – 3y + 5 II. 2. 100 – 5 + 12 +4 3. a + 8 – 36 6. – 8. (2x – 1)(4 + 3) 9. – 11. + 12. 2r – +4 – + –8 + + Find f(2) and f(–1) for each function. 1. f(x) = 4. f(x) = –2 –9 + 5x + 3 2. f(x) = 4 5. f(x) = –3 +8 + 2x – 1 – 10 3. f(x) = 9 –4 6. f(x) = – x+2 + 5x + 7 1 Polynomial Worksheet If the degree is even and the leading coefficient is positive, then f(x) → +∞ as x → –∞ f(x) → +∞ as x → +∞ If the degree is even and the leading coefficient is negative, then End Behavior of Polynomial Functions f(x) → –∞ as x → –∞ f(x) → –∞ as x → +∞ If the degree is odd and the leading coefficient is positive, then f(x) → –∞ as x → –∞ f(x) → +∞ as x → +∞ If the degree is odd and the leading coefficient is negative, then f(x) → +∞ as x → –∞ f(x) → –∞ as x → +∞ III. For each graph: a. Describe the end behavior, b. Determine whether it represents an odd-degree or an even-degree function c. State the number of real zeroes. 1. 4. 2. 3. 5. 6. 1 Polynomial Worksheet IV. Simplify the following: 1. · 2. 3. 5. (4 4. )(–5d ) 6. 8u 7. 8. 9 10. 11. –(4 ) 12. · · 1 Polynomial Worksheet V. Below is a graph with labeled points. Use the letters to identify key parts of the graph. You may use a point more than once. You don’t have to use all labeled points. a) x – intercept(s):________________________ b) local maximum(s): _____________________ c) interval where f(x) is increasing: (just use the letters) ______________________________________ d) absolute minimum(s) on the interval from points A to H ______________________________________ e) Does this function have an even or odd degree? Explain. f) Is the leading coefficient positive or negative? Explain. VI. Given the graph of the following polynomial, g(x): a) Is this an even or odd degree function? b) Is the leading coefficient positive or negative? 1 Polynomial Worksheet VII. Add/Subtract/Multiply the following polynomials. 2. (6w – 11 ) – (4 + 7 3. (4 x2 3x 2)(3x 2 2 x 1) 4. (x + y)( – 3xy + 2 5. (3r s) (r s) (r 3s) 6. 4a(3a 2b) 7. (4 x2 3 y 2 5xy) (8xy 6 x 2 3 y 2 ) 8. 3x 2 (2 x 2 9 x 6) 9. 4c2 d 3 (5cd 2 3c 2 d ) 10. ( x3 3x 2 1)(3x 2 6 x 2) 1. (3 + 1) + (8 – 8) ) )