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5 Cards in this Set
- Front
- Back
R1. If f(x) = -x^3 + 5x^2 + 4x -11, find f(3) by direct substitution and evaluation of the function.
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a.) Plug and chug
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R2. a.) Evaluate i^59
b.) Evaluate i^(-15) c.) Evaluate i^(500) d.) Write in terms of i and simplify: Sqrt (-63) e.) Plot -5+3i on the complex plane. f.) Write the complex conjugate of -17+3i g.) Subtract: (8-2i) - (3-11i) h.) Multiply: (5-7i)(2+8i) i.) Multiply: (12+i)(12-i) j.) Do the squaring: (12+i)^2 k.) Divide: (12+9i)/(3-4i) l.) Find the absolute value of 11 + 4i |
R2. a.) Evaluate i^59. This is easy if you remember that i^4 is 1.
b.) Evaluate i^(-15). Same thing, but on the denominator. c.) Evaluate i^(500). Again easy. d.) Write in terms of i and simplify: Sqrt (-63). Take the i out from under the radical sign. e.) Plot -5+3i on the complex plane. Real number -5 on the abscissa and imaginary number on the ordinate. f.) Write the complex conjugate of -17+3i. Simple g.) Subtract: (8-2i) - (3-11i). Just keep the signs straight and do it. h.) Multiply: (5-7i)(2+8i). Use the foil method. i.) Multiply: (12+i)(12-i). Again use foil. j.) Do the squaring: (12+i)^2. Again. k.) Divide: (12+9i)/(3-4i). Multiply by a clever form of 1 which is the complex conjugate of the denominator. l.) Find the absolute value of 11 + 4i |
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R3.
a.) Solve: 3x^2 + 4x + 10 = 0 b.) Write a quadratic equation with real-number coefficients if one of the solutions is 3+4i. c) Factor over the set of complex numbers: x^2 - 4x + 5. d.) Factor over the set of complex numbers: 25x^2+1 e.) Without actually solving the equation, find the sum of the solutions and the product of the solutions: 5x^2 + 13x + 79 = 0 |
R3.
a.) Solve: 3x^2 + 4x + 10 = 0; Figure it out directly or use the quadratic equation. b.) Write a quadratic equation with real-number coefficients if one of the solutions is 3+4i. Use the complex conj and the solution relationships. c) Factor over the set of complex numbers: x^2 - 4x + 5. Use the quadratic equation. d.) Factor over the set of complex numbers: 25x^2+1. Recognize the two squares. e.) Without actually solving the equation, find the sum of the solutions and the product of the solutions: 5x^2 + 13x + 79 = 0; Use the solution relationships. |
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R4.
a.) If P(x) = 5x^3 - 11x^2 + 8x + 9, find P(2) by synthetic substitution. b.) Plot the graph of P(x) = -2x^3 -x^2 _+ 6x + 8 in the domain -3 <_ x <_ 3. c.) Find all zeros of the function in part (b) d.) Find the remainder if P(x) = x^3 + 17 is divided by (x+2) e.) Sketch the graph of the quartic function with two distinct positive zeros, two distinct negative zeros, and a negative y intercept. |
R4.
a.) If P(x) = 5x^3 - 11x^2 + 8x + 9, find P(2) by synthetic substitution. Use the synthetic method to solve b.) Plot the graph of P(x) = -2x^3 -x^2 _+ 6x + 8 in the domain -3 <_ x <_ 3. First use the method. c.) Find all zeros of the function in part (b). Use the synthetic method to locate the zeros d.) Find the remainder if P(x) = x^3 + 17 is divided by (x+2). Use the formula. e.) Sketch the graph of the quartic function with two distinct positive zeros, two distinct negative zeros, and a negative y intercept. Sketch. |
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R5 Look at the word problems
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R5. Look at the word problems.
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