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Name______________________________________ practice test (skills) Write a polynomial function in standard form given the zeros: 1) -2, 3, 0, 0 2) -3 multiplicity 3 Expand using Pascal’s Triangle 3) (x – 3)5 4) (2x – 5)4 Divide using long division—write remainders in fractional form: 5) (2x3 + 13x2 + 17x + 10) (x + 5) 6) Divide using synthetic division—write remainders in fractional form: (x4 – 5x2 + 4x + 12) by (x + 2) A 7) Use synthetic division and the given factor to completely factor: y = x3 + 2x2 – 5x – 6; (x + 1) 8) Use synthetic division and the Remainder Theorem to find P(a): P(x) = 2x3 – x2 + 10x + 5; a = -5 9) Sketch a graph of the function paying attention to the end behaviors and the behavior of the graph at the x-intercepts. Y = x(x – 4)3(x + 5)2 A For each equation, state the number of complex roots, the possible number of real roots, and the possible rational roots: 10) x5 + 3x4 – x – 3 = 0 11) 2x4 – 3x3 + 4x + 1 = 0 # Complex: _________________ # Complex: __________________ # Possible reals: ______________________ # Possible reals:____________ Possible rationals:_______________________ Possible rationals:_________________ Solve each equation: 12) x3 – 2x2 + x = 0 13) 64x3 + 1 = 0 14) 2x4 + 14x2 – 36 = 0 15) 27x3 – 64 = 0 A 16) x3 - 3x2 + x + 5 = 0 17) x4 – 2x3 – 5x2 + 4x + 6 = 0 A