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Hw 19 Rational Roots Theorem & Graphing Polynomials

Homework which would help prepare for the exam. (It is pretty short fo...

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College Algebra (MATH 8)

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San José State University

Academic year: 2017/2018

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SJSU Math 08 Hw 19: Rational Roots Theorem Graphing Polynomials For questions let f (x) x3 x2 17x 15. 1. Use the Rational Roots Theorem to generate a list of potential zeroes. (a) (b) (c) (d) 2. Identify one actual zero, and use division to identify the other zeroes. (a) Zeroes: 2, 3 (b) Zeroes: 1, 5 (c) Zeroes: 5 (d) Zeroes: 1, 2, 3. Use the zeroes to determine the factored form of f (x). (a) f (x) (x 1)(x 3)(x 5) (b) f (x) (x 2)(x 3)(x 4) (c) f (x) (x 1)(x 2)(x 2) (d) f (x) (x 1)(x 3)(x 4) Page 1 of 9 Nov 15th SJSU Math 08 Hw 19: Rational Roots Theorem Graphing Polynomials 4. Determine the order and leading coefficient of f (x). (a) Order: x1 Leading Coefficient: 1 (b) Order: x3 Leading Coefficient: 1 (c) Order: x1 Leading Coefficient: 3 (d) Order: x3 Leading Coefficient: 3 5. Graph f (x). (a) (b) (c) (d) Page 2 of 9 Nov 15th SJSU Math 08 Hw 19: Rational Roots Theorem Graphing Polynomials 9. Determine the order and leading coefficient of f (x). (a) Order: x3 Leading Coefficient: 4 (b) Order: x3 Leading Coefficient: (c) Order: x4 Leading Coefficient: 4 (d) Order: x4 Leading Coefficient: 10. Graph f (x). (a) (b) (c) (d) Page 4 of 9 Nov 15th SJSU Math 08 Hw 19: Rational Roots Theorem Graphing Polynomials Nov 15th Let f (x) 2x4 7x3 5x2 9x 9. 11. Use the Rational Roots Theorem to generate a list of potential zeroes. (a) 2, 4, 8, 12, 12 , 23 (b) 2, 3, 4, 6, 8, 12, 21 , 32 (c) 3, 9, 21 , 23 , 92 (d) 2, 3, 6, 9, 21 , 23 , 29 12. What are the roots of this function? Hint: If you reach a point where the equation is no longer solvable, then you have already found all of the possible solutions. (a) Roots 1, 3 (b) Roots (c) Roots 1, 3, 9, 3 2 (d) Roots 9, 2 13. Write f (x) in its factored form. (a) f (x) (x 1)(x 3)(x 9)(x 32 ) (b) f (x) (x 1)(x 3)(x 9)(x 12 ) (c) f (x) (x 1)(x 3)(2x2 x 3) (d) f (x) (x 1)(x 3)(2x2 3x 1) Page 5 of 9 SJSU Math 08 Hw 19: Rational Roots Theorem Graphing Polynomials Nov 15th Let f (x) x3 5x2 4. 16. Use the Rational Roots Theorem to generate a list of potential zeroes. (a) 2, 4, 8, 12, 21 (b) 2, 3, 4, 6, 8, 12, 23 (c) 2, 3, 4, 5, 10, 12 (d) 2, 4 17. Identify the zeroes of this polynomial. Hint: If factoring work when you reach the x2 part, try the quadratic formula. (a) Zeroes: 1, 1, 21 (b) Zeroes: 1, (c) Zeroes: 1, 2 2 2, 2 2 2 (d) Zeroes: 1, 3 5, 3 5 18. What is the factored form of f (x)? (a) f (x) (x 1)(x (2 2 2))(x (2 2 2)) (b) f (x) (x 1)(x (3 5))(x (3 5)) (c) f (x) (x 1)(x 4)(x 23 ) (d) f (x) (x 1)(x 1)(x 21 ) Page 7 of 9 SJSU Math 08 Hw 19: Rational Roots Theorem Graphing Polynomials Nov 15th For questions 19 23, choose which graph best represents the given function. (a) (b) (c) (d) (e) (f) (g) (h) Note: you do not need to find for the following problems. 19. Sketch the graph of the function: f (x) 10x 2x4 3x5 20. Sketch the graph of the function: f (x) 3 x3 21. Sketch the graph of the function: g(x) 10x4 20x3 22. Sketch the graph of the function: Z(t) 100t t2 23. Sketch the graph of the function: A(B) 300, B 4 100, 2 Page 8 of 9

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