Download Polynomials Test Review 1) Find the equation in s

Academic Algebra 2
Name:________________________
Date: __________
Block:______
Polynomials Test Review
1)
Find the equation in standard form that would have each of the following sets of roots:
(a) x = –1; x = 2; x = –3
(b) x = 2; x = –2; x = − 5
2
2) If –3 is a root, find the other roots and write in factored form: f ( x) = x 3 − 7 x 2 − 5 x + 75
3) Given the following graphs, write the function in factored:
(a)
(b) Degree 3:
3
2
4) Given the following equation, state the roots and multiplicity of each root: y = ( x + 2) ( x − 3)
5)
Given the following equation, state the zeroes and the multiplicity of each zero:
f ( x) = x 5 − 9 x 4 + 27 x 3 − 27 x 2
6) Given the following function, state the number of zeroes, the number of real zeroes, and the number of
imaginary root: f ( x) = x 4 − x 2 − 3
7) Given the following function, state the total number of zeros, the number of real roots, any multiplicity
and where they occur, and the number of imaginary root: f (x) = x5 − 2x3 − 2x2 − 3x − 2
8)
9)
Identify all the zeroes: f (x) = (x + 4) 2 (x − 3) 3 (x + 9) : _____________________________
Which of the following is a polynomial function:
(a) h( x) =
1 3
x + 2x
4
(b) f ( x) = 3.4 x 9 + 2 x
(c) g( x) = 5x − 7 x
(d) k(x) = 2x 3 − x −4
11)
Use the polynomial: f ( x) = 3x 5 + 1 − 2 x 2 + 7 x 6
(a) Write the polynomial in Descending order: _____________________________
(b) State the degree: _____________
(c) State the Leading Coefficient: ___________
12) Graph the function and fill in the blanks.
f (x) = x3 − 4x2 + 7
Zeros__________________________________
Y-intercept_____________________________
Maximum(s)_____________________________
Minimum(s)_____________________________
Domain________________________________
Range_________________________________
End Behavior___________________________
_____________________________________
Increasing/Decreasing:____________________
______________________________________
______________________________________
13)) Match each grap
[A]
ith its description:
[B]
___ 8th-degree polynomial, negative leading coefficient.
___ 7th-degree polynomial, negative leading coefficient.
___ 5th-degree polynomial, positive leading coefficient.
___ 4th-degree polynomial, positive leading coefficient.
[C]
[D]
20) Match each graph with its description:
[A]
[B]
___ 8th-degree polynomial, negative leading coefficient.
___ 7th-degree polynomial, negative leading coefficient.
___ 5th-degree polynomial, positive leading coefficient.
___ 4th-degree polynomial, positive leading coefficient.
[C]
[D]