Chapter 13 Study Guide
Name:__________________________
1) Create an algebraic expression that fits each of the following descriptions.
a) A Binomial whose degree is 4.
b) A monomial with no coefficient.
c) A Polynomial with 4 terms & degree 5
d) A monomial with no degree.
2) Identify each of the following as a Monomial, Binomial, Trinomial, or Polynomial. (Be accurate)
a) 3𝑥 + 8
b) 15𝑥𝑦 − 7𝑥 + 5𝑥 − 2
c) 12𝑥 2 𝑦𝑧 3
d) 2𝑥 2 + 3𝑥 − 9
3) Find the degree of each of the following algebraic expressions.
a) 12𝑥 2 𝑦𝑧 3
b) 2𝑥 4 + 3𝑥 − 9
c) 2𝑥 + 38
4) Write each of the following in standard form.
a) 2𝑥 − 3𝑥 5 + 7𝑦𝑥
b) 10𝑦𝑥 − 5𝑥 4
c) −6𝑡 3 + 4 + 5𝑡 3
5) Simplify each of the following expressions using addition, subtraction, & multiplication.
a) (4𝑚2 + 9𝑚) − (2𝑚2 − 6)
b) (−𝑥 2 + 5𝑥 − 12) + (2𝑥 2 − 6)
c) (2𝑥 + 1)(𝑥 + 8)
d) (𝑥 + 3)(4𝑥 2 − 2𝑥 + 1)
e) (5𝑥 + 3𝑦 + 7) + (−2𝑥 + 7𝑦)
f) (−2𝑥 + 3) − (−3𝑥 2 − 2𝑥 − 7)
6) Simplify each of the following Radicals
a) √144𝑥 2
b) √75𝑥𝑦 2
c) √104
7) Estimate each of the following Radicals
a) √7
8) Factor out the GCF
a) 𝑚2 − 9𝑚
b) √109
c) √27
b)24𝑤 2 + 16
d) √50
c)20𝑥𝑦 2 − 50𝑦 2 + 30𝑦
9) Factor each using the diamond method
a) 𝑥 2 + 7𝑥 + 10
b) 𝑥 2 − 15𝑥 + 14
c) 𝑥 2 − 3𝑥 − 40
10) Factor each using the long diamond method
a) 2𝑥 2 + 3𝑥 − 9
b) 2𝑥 2 + 11𝑥 + 5
c) 6𝑥 2 + 7𝑥 − 49
11) Factor each using Difference of Squares
a) 𝑥 2 − 49
b) 4𝑥 2 − 25
c) 9𝑦 2 − 100𝑥 4
12) Factor each using Perfect Square Trinomials
a) 𝑥 2 − 6𝑥 + 9
b) 4𝑥 2 + 20𝑥 + 25
c) 3 + 6𝑥 + 3𝑥 2
13) Factor each by grouping.
a) 12𝑥 3 − 9𝑥 2 + 4𝑥 − 3
c) 35𝑥𝑦 + 5𝑥 − 56𝑦 − 8
b) 2𝑝3 + 5𝑝2 + 6𝑝 + 15
14) Solve for the Zeroes in each of the following using factoring.
a) 𝑥 2 + 2𝑥 − 8 = 0
b) 2𝑥 2 + 8𝑥 = 0
c) 𝑡 2 + 15𝑡 = −50
15) Factor each of the following completely using any method. (Flow)
a) 200𝑥 2 − 50
b) 𝑥 8 − 1
c) −𝑥 2 − 12𝑥 − 32
d) 2𝑥 2 − 14𝑥 + 24
e) 6𝑥 2 − 4𝑥 − 10
f) 𝑥 2 + 2𝑥𝑦 + 𝑦 2
Review:
16) Using each of the parabolas drawn below identify each of the key features listed.
Opens up or down
Vertex
Max/Min Point
Axis of Symmetry
Domain
Range
Zeroes
y-intercept
17) Graph each of the following using at least 3 points. Identify Vertex, zeroes, & yint.
a)
b)
18) Find the vertex in Vertex Form.
a)
19) Find the Zeroes in Factored Form.
a)
20) Calculate the distance btwn points.
a) (9,3) & (-2,7)
21) Calculate the midpoint.
a) (8,3) & (-2,7)