Algebra Semester 2 Final
Chapter 5 Test #1:
Write the polynomial function in Standard Form, classify it by degree, and determine the end
behavior.
3x - 6x^2 + 8 - 5x^4 - ANS Standard Form: -5x^4 - 6x^2 + 3x + 8
Classify by Degree: Quartic
End Behavior: Down, Down
Chapter 5 Test #3
Use factoring to find the zeros of the function.
P(x)= x^2 - 5x + 6 - ANS x = 2 and x = 3
Chapter 5 Test #4
Use factoring to find the zeros of the function.
P(x) = 6x^2 - 7x - 5 - ANS x = 5/3 and x = -1/2
Chapter 5 Test #5
Divide using long division. (Show your work)
(2x^3 + 2x^2 - 7x + 21) / (x + 3) - ANS 2x^2 - 4x + 5 + 6/x+3
Chapter 5 Test #6
Divide using synthetic division. Rewrite as a polynomial with a remainder (You should get the
same answer as the last problem).
(2x^3 + 2x^2 - 7x + 21) / (x + 3) - ANS 2x^2 - 4x + 5 + 6/x+3
Chapter 5 test #7
List all the possible rational roots of P(x) given by the Rational Root Theorem
3x^5 - 5x^3 + 8x^2 - x + 4 - ANS Possible Roots:
, + 1, - 1, +4, -4, +2, -2, +1/3, -1/3, +4/3, -4/3, +2/3, -2/3
Chapter 5 Test #8
Determine the possible number of positive real zeros and negative real zeros for the polynomial
function given by using Descartes' Rules of Signs.
P(x) = 4x^5- 2x^4 - 3x^2 + x - 7 - ANS Possible number of positive real roots: 3 or 1
Possible number of negative real roots: 0
Chapter 5 Test #13
Write a polynomial function with the given zeros. Put it in standard form, so yes you need to
carefully multiply them out.
x = 2 , -4, 4 - ANS x^3 - 2x^2 - 16x + 32
Chapter 5 Test #14
Write a polynomial function with the given zeros. Put it in standard form, so yes you need to
carefully multiply them out.
x = 5i, 3 - ANS x^3 - 3x^2 + 25x - 75
Chapter 5 test #15/16
Use you graphing calculator to find the relative max, relative min and zeros. Round answers to
NEAREST HUNDREDTH.
P(x) = -3x^3 + 4x - 1 - ANS Relative Maximum(s): (0.67, 0.78)
Relative Minimum(s): (-0.67, -2.78)
Zero(s): (1, 0) (-1.26, 0) (026, 0)
Chapter 5 Test #19
A polynomial P(x) has rational coefficients. Name required additional roots of P(x) given the
following roots.
3, 2-(root 5) and 6i - ANS -6i and 2 + (root 5)
Chapter 5 Test #20
Find the total number of roots for the equation.
Chapter 5 Test #1:
Write the polynomial function in Standard Form, classify it by degree, and determine the end
behavior.
3x - 6x^2 + 8 - 5x^4 - ANS Standard Form: -5x^4 - 6x^2 + 3x + 8
Classify by Degree: Quartic
End Behavior: Down, Down
Chapter 5 Test #3
Use factoring to find the zeros of the function.
P(x)= x^2 - 5x + 6 - ANS x = 2 and x = 3
Chapter 5 Test #4
Use factoring to find the zeros of the function.
P(x) = 6x^2 - 7x - 5 - ANS x = 5/3 and x = -1/2
Chapter 5 Test #5
Divide using long division. (Show your work)
(2x^3 + 2x^2 - 7x + 21) / (x + 3) - ANS 2x^2 - 4x + 5 + 6/x+3
Chapter 5 Test #6
Divide using synthetic division. Rewrite as a polynomial with a remainder (You should get the
same answer as the last problem).
(2x^3 + 2x^2 - 7x + 21) / (x + 3) - ANS 2x^2 - 4x + 5 + 6/x+3
Chapter 5 test #7
List all the possible rational roots of P(x) given by the Rational Root Theorem
3x^5 - 5x^3 + 8x^2 - x + 4 - ANS Possible Roots:
, + 1, - 1, +4, -4, +2, -2, +1/3, -1/3, +4/3, -4/3, +2/3, -2/3
Chapter 5 Test #8
Determine the possible number of positive real zeros and negative real zeros for the polynomial
function given by using Descartes' Rules of Signs.
P(x) = 4x^5- 2x^4 - 3x^2 + x - 7 - ANS Possible number of positive real roots: 3 or 1
Possible number of negative real roots: 0
Chapter 5 Test #13
Write a polynomial function with the given zeros. Put it in standard form, so yes you need to
carefully multiply them out.
x = 2 , -4, 4 - ANS x^3 - 2x^2 - 16x + 32
Chapter 5 Test #14
Write a polynomial function with the given zeros. Put it in standard form, so yes you need to
carefully multiply them out.
x = 5i, 3 - ANS x^3 - 3x^2 + 25x - 75
Chapter 5 test #15/16
Use you graphing calculator to find the relative max, relative min and zeros. Round answers to
NEAREST HUNDREDTH.
P(x) = -3x^3 + 4x - 1 - ANS Relative Maximum(s): (0.67, 0.78)
Relative Minimum(s): (-0.67, -2.78)
Zero(s): (1, 0) (-1.26, 0) (026, 0)
Chapter 5 Test #19
A polynomial P(x) has rational coefficients. Name required additional roots of P(x) given the
following roots.
3, 2-(root 5) and 6i - ANS -6i and 2 + (root 5)
Chapter 5 Test #20
Find the total number of roots for the equation.
