Algebra 2/TrigHigher Order Polynomials

Test Review

Match the polynomial function with its graph.

Answers

Match the roots with the graphs.

x = -1, 0 , 1

x = -2, 0, 2

x = -2, -1, 1, 2

Answers

x = -1, 0 , 1x = -2, 0,

2

x = -2, -1, 1, 2

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.

a < 0; x = 2, -1,

a > 0; x = 0, 6 (double root),

3 5

2i

Answers

4 3 27 8 8 8x x x x

Answers5 4 3 212 40 48 144x x x x x

Write the polynomial equation with the following roots.

x = 2 (double root)

x = 0 (triple root), 2, -3

x =

5

6 3

Answers

. 4 3 2( ) 4 20 20f x x x x x

Answers

.5 4 3( ) 6f x x x x

Answers

.2( ) 12 33f x x x

Find the roots/zeros of the following polynomials by using any algebraic method.

. 4 2( ) 4 5f x x x

Answers

x = ± 5, 1i x

Find the roots/zeros of the following polynomials by using any algebraic method.

. 3 2( ) 4 4 15f x 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 13 3f x x x x

Answers P/q : ±1, ±3, ±1/2,

±3/2

x =

1 7 61,2 2

x

List all the possible rational roots. Then find the roots/zeros of the following polynomials by using any algebraic method.

. 4 3 2( ) 6 54 72f x x x 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 25 12f x x x x

Answers p/q = ±1, ±2, ±3, ±4, ±6, ±12, ±1/2,

±3/2

x = 3, x = ½, x = -4

Find the roots/zeros of the following polynomials by using a graphing calculator.

. 3 2( ) 2 5 9 8f x 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( ) 3 13 39 36 108, ( 3)f x x x x x x x

Answers( 3)( 3)( 2)( 2)( 3)x 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.

Zeros: Relative Maximums: Relative Minimums: Increasing: Decreasing:

4 3( ) 4 2 f x x x

Determine the following information using a graphing calculator.

Zeros: (.860, 0) and (3.968,0)

Relative Maximums: none Relative Minimums: (3,-25) Increasing: (3, ∞) Decreasing: (- ∞ , 3)

4 3( ) 4 2 f x x x

Determine the following information using a graphing calculator.

Zeros: Relative Maximums: Relative Minimums: Increasing: Decreasing:

5 3( ) 6 2 3 f x x x x

Determine the following information using a graphing calculator.

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,∞)

5 3( ) 6 2 3 f x x x x