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Solving Quadratic Equations by Factoring Worksheet

Solving Quadratic Equations by Factoring Worksheet
  • Page 1
 1.  
Solve the equation (a - 5)(a + 5) = 0.
a.
5 and - 5
b.
5 and 5
c.
-5 and + 5
d.
- 5 and 5


Solution:

(a - 5)(a + 5) = 0
[Original equation.]

(a - 5) = 0 or (a + 5) = 0
[Set each factor equal to zero.]

a = 5 or a = -5
[Solve for a.]

The solutions of the equation (a - 5)(a + 5) = 0 are 5 and -5.


Correct answer : (1)
 2.  
What is the x-coordinate of the vertex of the graph of y = 5(4x + 9)(x + 3)?
a.
- 20 7
b.
- 8 21
c.
- 21 8
d.
- 22 9


Solution:

y = 5(4x + 9)(x + 3)
[Original equation.]

0 = 5(4x + 9)(x + 3)
[Substitute y = 0.]

(4x + 9) = 0 or (x + 3) = 0
[Solve for x.]

The x-intercepts are -9 / 4 and -3.

The x-coordinate of the vertex is the average of the x-intercepts.

x = [(-94) + (-3)]/2 = -218

The x-coordinate of the vertex of the graph of y = 5(4x + 9)(x + 3) is –21 / 8


Correct answer : (3)
 3.  
The entrance door of a prison is in an inverse U-shape, similar to a parabola. If the shape of the door is modeled by a function y = (-4/32)(2x + 4)(2x - 4), then what is the width of the door at the base?
a.
3
b.
4
c.
5
d.
6


Solution:

y = (-4/32)(2x + 4)(2x - 4)
[Original equation.]

0 = (-4/32)(2x - 4)(2x + 4)
[Substitute 0 for y to get x-intercepts.]

(2x - 4) = 0 or (2x + 4) = 0
[Set each factor equal to zero.]

x = 2 or x = - 2
[Solve for x.]

The width of the door at the base is 2 + 2 = 4 ft.
[Take positive value because the width cannot be negative.]


Correct answer : (2)
 4.  
Solve: (e + 5)2 = 0
a.
-25
b.
25
c.
-5


Solution:

(e + 5)2 = 0
[Original equation.]

(e + 5)(e + 5) = 0
[Split into factors.]

(e + 5) = 0
[Equate each factor to zero.]

e = -5
[Solve for e.]

The solution of the equation (e + 5)2 = 0 is -5.


Correct answer : (4)
 5.  
Solve: (b - 7)2 = 0
a.
7
b.
12
c.
-12
d.
-7


Solution:

(b - 7)2 = 0
[Original equation.]

(b - 7)(b - 7) = 0
[Split into factors.]

b - 7 = 0
[Equate each factor to zero.]

b = 7
[Simplify.]

The solution of the equation (b - 7)2 = 0 is 7.


Correct answer : (1)
 6.  
Solve: (10c - 9)2 = 0
a.
9 10
b.
10 9
c.
- 10 9
d.
- 9 10


Solution:

(10c - 9)2 = 0
[Original equation.]

(10c - 9)(10c - 9) = 0
[Split into factors.]

(10c - 9) = 0
[Equate each factor to zero.]

10c = 9
[Simplify.]

c = 910
[Divide each side by 10.]

The solution of the equation (10c - 9)2 = 0 is 9 / 10.


Correct answer : (1)
 7.  
Solve: (d - 5)(5d - 11) = 0
a.
- 5 and - 11 5
b.
5 and - 11 5
c.
5 and 11 5
d.
-5 and 11 5


Solution:

(d - 5)(5d - 11) = 0
[Original equation.]

(d - 5) = 0 or (5d - 11) = 0
[Equate each factor to zero.]

d = 5 or d = 115
[Simplify.]

The solutions of the equation (d - 5)(5d - 11) = 0 are 5 and 11 / 5.


Correct answer : (3)
 8.  
Solve: f(f + 3) = 0
a.
3 and -3
b.
0 and 3
c.
5 and -5
d.
0 and -3


Solution:

f (f + 3) = 0
[Original equation.]

f = 0 or (f + 3) = 0
[Equate each factor to zero.]

f = 0 or f = -3
[Simplify.]

The solutions of the equation f(f + 3) = 0 are 0 and -3.


Correct answer : (4)
 9.  
Solve: (g - 3)(g + 3)(g - 4) = 0
a.
3 and -3 or -4
b.
-3 and -3 or 4
c.
3, -3 and 4
d.
3 and 3 or -4


Solution:

(g - 3)(g + 3)(g - 4) = 0
[Original equation.]

(g - 3) = 0 or (g + 3) = 0 or (g - 4) = 0
[Equate each factor to zero.]

g = 3 or g = -3 or g = 4
[Simplify.]

The solutions of the equation (g - 3)(g + 3)(g - 4) = 0 are 3, -3 and 4.


Correct answer : (3)
 10.  
Solve: (4h - 3)(5h - 4)(6h + 5) = 0
a.
-3/4, -4/5 and -5/6
b.
3/4, 4/5 and -5/6
c.
-3/4, -4/5 and 5/6
d.
3/4, 4/5 and 5/6


Solution:

(4h - 3)(5h - 4)(6h + 5) = 0
[Original equation.]

(4h - 3) = 0 or (5h - 4) = 0 or (6h + 5) = 0
[Equate each factor to zero.]

4h = 3 or 5h = 4 or 6h = -5
[Simplify.]

h = 3 / 4 or h = 4 / 5 or h = -5 / 6
[Simplify to get the value of h.]

The solutions of the equation (4h - 3)(5h - 4)(6h + 5) = 0 are 3 / 4, 4 / 5 and - 5 / 6.


Correct answer : (2)

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