High Order Polynomial Equations Test Review
Prepare for an Algebra 2/Trig test on higher order polynomial functions by matching functions with graphs, roots with graphs, and solving equations from given roots. Explore various polynomial scenarios and solutions with detailed answers.
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Algebra 2/Trig Higher Order Polynomials Test Review
Match the polynomial function with its graph.
Match the roots with the graphs. x = -1, 0 , 1 x = -2, 0, 2 x = -2, -1, 1, 2
Answers x = -2, 0, 2 x = -2, -1, 1, 2 x = -1, 0 , 1
Write the equation with the following roots, then draw a rough sketch of the graph. a < 0; x = 2, -1
Answers -(x 2) (x + 1) -(x2 +1x -2x -2) -(x2 -1x -2) -x2 +1x +2
Write the equation with the following roots, then draw a rough sketch of the graph. 3 5 a < 0; x = 2, -1, a > 0; x = 0, 6 (double root), 2i
Answers + + 4 3 2 7 8 8 8 x x x x
Answers 12 x + + 5 4 3 2 40 48 144 x x x x
Write the polynomial equation with the following roots. x = 2 (double root) 5 x = 0 (triple root), 2, -3 x = 6 3
Answers = + . 4 3 2 ( ) f x 4 20 20 x x x x
Answers = + 5 4 3 . ( ) f x 6 x x x
Answers = + 2 ( ) f x 12 33 x x .
Find the roots/zeros of the following polynomials by using any algebraic method. = + 4 2 ( ) f x 4 5 x x .
Answers x = x = 5, 1 i
Find the roots/zeros of the following polynomials by using any algebraic method. = + + 3 2 ( ) f x 4 4 15 x x x .
Answers x = 0, x = -3/2, x = 5/2
List all the possible rational roots. Then find the roots/zeros of the following polynomials by using any algebraic method. 3 2 ( ) 2 13 f x x x = + + 13 3 x .
Answers P/q : 1, 3, 1/2, 3/2 x = 1 7 61 = , x 2 2
List all the possible rational roots. Then find the roots/zeros of the following polynomials by using any algebraic method. ( ) 6 f x x x = + 4 3 2 54 72 x x .
Answers p/q = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 x = -2, x = -4, x = -3, x = 3
List all the possible rational roots. Then find the roots/zeros of the following polynomials by using any algebraic method. 3 2 ( ) 2 f x x x = + + 25 12 x .
Answers p/q = 1, 2, 3, 4, 6, 12, 1/2, 3/2 x = 3, x = , x = -4
Find the roots/zeros of the following polynomials by using a graphing calculator. = + + 3 2 ( ) f x 2 5 9 8 x x x .
Answers x = -1.661, x = .695, x = 3.465
Given one for the factors, find all the factors of f. . = + + + + 5 4 3 2 ( ) f x 3 13 39 36 108, ( 3) x x x x x x
Answers ( 3)( x + + + 3)( 2)( 2)( 3) x x x x
Fill in the following information given the graph below. Zeros: Relative Maximums: Relative Minimums: Increasing: Decreasing:
Fill in the following information given the graph below. ANSWERS MAY VARY Zeros: (-2.2, 0) Rel Max: (1,-2) Rel Min: (-1, -6) Inc: (-1,1) Dec: (- ,-1)U(1, )
Determine the following information using a graphing calculator. = + f x x x 4 3 ( ) 4 2 Zeros: Relative Maximums: Relative Minimums: Increasing: Decreasing:
Determine the following information using a graphing calculator. = f x x + 4 3 ( ) 4 2 x Zeros: (.860, 0) and (3.968,0) Relative Maximums: none Relative Minimums: (3,-25) Increasing: (3, ) Decreasing: (- , 3)
Determine the following information using a graphing calculator. = + + x x x 5 3 ( ) f x 6 2 3 Zeros: Relative Maximums: Relative Minimums: Increasing: Decreasing:
Determine the following information using a graphing calculator. = + + 5 3 ( ) f x 6 2 3 x x x Zeros: (-2.321,0), (-1,0), (2.423,0) Rel Max: (-.339,3.449), (1.867,15.629) Rel Min: (-1.867,-9.629), (.339,2.551) Inc: (-1.867,-.339)U(.339,1.867) Dec: (- ,-1.867)U(-.339,.339)U(1.867, )
