19. List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros): = 6x4 - + 8x + 12 S(x) x2 20. Find all rational zeros of the polynomial. = - 8x2 + 17x - 10 P(x) x3 21. A polynomial is P = -x3 + 2x2 + 21x + 18 P(x) (a) Find all the real of P. (b) Sketch the graph of P. 22. Use Descartes' Rule of to determine how many positive and how many negative real zeros the polynomial can have. Then determine the possible total number of real zeros. = -4x3 + 7x2 - 4x + 8 P(x) = - - 4x - 5 P(x) x3 x2 23. Evaluate the expression and write the result in the form a + bi. (4 - 5i) -1 1602 i 24. Find all solutions of the equation and express them in the form + a bi. 25. For polynomial is given: = + 64x2 , (x) = 125, = - 5x2 6, = + 7x3 - P P(x) x4 P x3 P(x) x4 P(x) x6 – – 8 (a) Find all zeros of real and complex. P, (b) Factor completely. P 26. Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. has degree 2, and zeros 2 + and 2 - P i i. has degree 2, and and . P has degree 3, and 4 and Q i.
19. List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros): S(x) = 6x4 - x2 + 8x + 12 20. Find all rational zeros of the polynomial. P(x) = x3 - 8x2 + 17x - 10 21. A polynomial P is P(x) = -x3 + 2x2 + 21x + 18 (a) Find all the real of P. (b) Sketch the graph of P. 22. Use Descartes' Rule of to determine how many positive and how many negative real zeros the polynomial can have. Then determine the possible total number of real zeros. P(x) = -4x3 + 7x2 - 4x + 8 P(x) = x3 - x2 - 4x - 5 23. Evaluate the expression and write the result in the form a + bi. (4 - 5i) -1 i 1602 24. Find all solutions of the equation and express them in the form a + bi. 25. For polynomial P is given: P(x) = x4 + 64x2 , P (x) = x3 – 125, P(x) = x4 - 5x2 – 6, P(x) = x6 + 7x3 - 8 (a) Find all zeros of P, real and complex. (b) Factor P completely. 26. Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. P has degree 2, and zeros 2 + i and 2 - i. P has degree 2, and and . Q has degree 3, and 4 and i.
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