1. 1. Simplify (Place answer in standard form):
Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
1. Simplify (Place answer in standard form):
(8x2 – 5) + (3x + 7) – (2x2 – 4x)
NOTE: The subtraction must be distributed to each term
6x2
+ 2
+ 7x
Place in standard form
6x x
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2. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
2. Simplify (Place answer in standard form):
(2a3 – 6a ) ─ (5a2 ─ 2a )
NOTE: The subtraction must be distributed to each term
2a3
– 4a
+ 0
– 5a2
Place in standard form
2a3 – 5a2 – 4a

3. 3. Simplify (Place answer in standard form):
Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
3. Simplify (Place answer in standard form):
NOTE: To square a binomial, you must multiply it
by itself
(5x – 2)2
( )
( ) 5x 2 –
Combine
25x 2 –
10x –
10x + 4
25x2 – 20x

4. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
4. Simplify (Place answer in standard form):
(m – 3)(7 – 2m m) 7m
– 2m3
+ 5m2
– 15m
+ 6m2
– 21
Combine like terms
– 8m
– 2m3
+ 11m2
– 21
Place in standard form
− 2m3
+ 11m2
– 8m
– 21

5. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
5. Given:
a) Simplify and put in standard form.
− 2t ( t2 )
− 2t ( t2 )
− 6t
– 14t3
− 14t3 – 6t
Place in standard form
b) Identify the degree of the polynomial:
The degree is the largest
exponent of the polynomial 3

6. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
5. Given:
c) Name the polynomial based on the degree.
− 2t ( t2 )
cubic
Since the polynomial is of
Degree 3
d) Identify the type of polynomial based on the number of terms.
There are two terms in the polynomial
binomial

7. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
6. a) Factor: x x = 0
* Identify a, b and c
a = 1
, b = 10
, c = 25
* You are looking for two numbers that do the following
Add up to give you b and multiply to give you c
Notice: = 10
and • 5 = 25
(x + 5)(x + 5) = Or (x + 5)2 = 0
Use the zero product property to find the
solutions
(x + 5)(x + 5) = 0
Factored form
x = 0
Zero Product Property
– 5
– 5
Subtract
x = − 5

8. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
6. Factor: x x = 0
c) Check your solution
x = − 5
Equation
x x = 0
Substitute
(− 5) (− 5) = 0
Simplify
25 – = 0
− = 0
0 = 0
Check

9. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
7. a) Factor: x2 – 5x – 24 = 0
* Identify a, b and c
a = 1
, b = − 5
, c = − 24
* You are looking for two numbers that do the following
Add up to give you b and multiply to give you c
Notice: (− 8) = − 5
and • (− 8) = − 24
(x + 3)(x – 8) = 0
Use the zero product property to find the
solutions
(x + 3)(x – 8) = 0
Factored form
x = and x – 8 = 0
Zero Product Property
Subtract
– 3
– 3
+ 8
+ 8
Add
x = − 3
x = 8

10. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
8. a) Factor: x2 – 81 = 0
Difference of two perfect squares pattern
* a2 – b2 = (a ─ b)(a + b)
* Identify the a and the b by taking the
square root of each term
Notice, x2 x
= a 81 9
= b
* Substitute into the difference of two
perfect square pattern
(x – 9)(x + 9) = 0

11. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
8. Factor: x2 – 81 = 0
b) Use the zero product property to find the solutions:
(x – 9)(x + 9) = 0
Factored form
x – 9 = and x = 0
Zero Product Property
Add
+ 9
+ 9
– 9
– 9
Subtract
x = 9
x = − 9

12. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
Given: 4x2 – 14x = 0
a) Factor out the common monomial
* The greatest common monomial is 2
2(2x2 – 7x + 3) = 0
Factor out a 2

13. b) Factor the resulting trinomial
Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
Given: 4x2 – 14x = 0
b) Factor the resulting trinomial
2(2x2 – 7x + 3) = 0
* Identify a, b and c
a = 2
, b = − 7
, c = 3
* You are looking for two numbers that do the following
Add up to give you b and multiply to give you a • c
Notice: − (−1) = − 7
and − 6 • (− 1) = 6
* Build fractions using the leading term less one degree as
your numerator and −6 and −1 as your denominators 1 2x 2x x 2x
and
and
Reduce −6 −1 −3 −1 −3
* Write your final factorization using the two fractions
2(x – 3)(2x – 1) = 0

14. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
Factor: 4x2 – 14x = 0
c) Use the zero product property to find
the solutions
2(x – 3)(2x – 1) = 0
Factored form
x – 3 = and 2x – 1 = 0
Zero Product Property
Add
+ 3
+ 3
+ 1
+ 1
Add
x = 3
2x = 1
Divide 2 2 1
x = 2

15. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
10. Using the Vertical Motion Model h = − 16t s
where
h = height of the object at time t
t = time in seconds
s = initial height
You are standing on a cliff 784 feet high and drop your cell phone. How long will it take until your phone hits the ground below (h = 0)?
h = 0
* Identify h, t and s
t = t (need to find)
s = 784
Isolate t2
0 = − 16t
Substitute
– 784
– 784
Subtract
− = − 16t2
Divide
−16
−16
49 = t2

16. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
10. Using the Vertical Motion Model h = − 16t s
where
h = height of the object at time t
t = time in seconds
s = initial height
You are standing on a cliff 784 feet high and drop your cell phone. How long will it take until your phone hits the ground below (h = 0)? +
49 = t2
Square root +
7 = t
* Time is always positive
7 = t
It will take 7 seconds for the
phone to hit the ground

17. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
11. Complete the following given:
a = 1
y = x x – 8
b = 2
* Identify a, b and c
c = − 8
* The vertex is the highest or lowest point on a parabola
a) Find the vertex
− b
Formula to find x-value of vertex
x = 2a
− (2)
Substitute
2(1)
− 2
Simplify 2
x = − 1
x-value of vertex

18. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
11. Complete the following given:
y = x x – 8
a = 1
b = 2
a) Find the vertex
c = − 8
x = − 1
* Substitute into the quadratic equation to find y
y = x x – 8
Equation
y = (−1) (− 1) – 8
Substitute
y = 1 – 2 – 8
Simplify
y = − 1 – 8
y = − 9
Vertex (−1, − 9)

19. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
11. Complete the following given:
a = 1
y = x x – 8
b = 2
c = − 8
b) Find the y - intercept
* Where the graph crosses the
y-axis, NOTE: x = 0
y = x x – 8
y = (0) (0) – 8
y = – 8
y = − 8
(0, − 8)

20. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
11. Complete the following given:
a = 1
y = x x – 8
b = 2
c = − 8
c) Let y = 0, factor and solve using the zero product property
* You are looking for two numbers that do the following
Add up to give you b and multiply to give you c
Notice: (− 2) = 2
and • (− 2) = − 8
0 = x2 – 6x + 8
Let y = 0
0 = (x + 4)(x – 2)
Factored form
x = and x – 2 = 0
Zero Product Property
Subtract
– 4
– 4
+ 2
+ 2
Add
x = − 4
x = 2

21. Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
11. Complete the following given:
a = 1
y = x x – 8
b = 2
c = − 8
Identify the x – intercepts using the results
from part c
x = − 4
x = 2
From part c.
* The zeros of the quadratic are also the x - intercepts
* Notice the x – intercepts have a y – coordinate of 0
(− 4, 0) and (2, 0)

22. You are a Math Super Star
Algebra I Concept Test # 15 – Solving Quadratic Equations by Factoring Practice Test
11. Complete the following given:
y = x x – 8
You are a
Math Super Star
e) Graph
* Plot the following
ordered pairs:
Vertex: (− 1, − 9)
y – intercept: (0, − 8)
x – intercepts:
(− 4, 0) and (2, 0)