To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Solving Equations by Factoring Worksheet

Solving Equations by Factoring Worksheet
  • Page 1
 1.  
Find the value of x, which satisfies the equation |x2 + 7x| + 2x2 - 6 = 0 if x2 + 7x > 0.
a.
- 3 2
b.
2
c.
2 3
d.
- 3


Solution:

|x2 + 7x| + 2x2 - 6 = 0 for x2 + 7x > 0

x2 + 7x + 2x2 - 6 = 0

3x2 + 7x - 6 = 0
[Simplify.]

(x + 3)(3x - 2) = 0
[Split into factors.]

x + 3 = 0 or 3x - 2 = 0
[Equate each factor to zero.]

x = - 3 or x = 2 / 3
[Simplify.]

Therefore, x = 2 / 3
[As x = - 3 does not satisfy the condition x2 + 7x > 0.]


Correct answer : (3)
 2.  
Andrew's garden is square shaped and Gary's garden is rectangular in shape. The length of the rectangular garden is longer by a ft, and its width is b ft shorter than the square garden. If both gardens have the same area, then find the dimensions of the rectangular garden. [a = 9 ft and b = 7 ft.]
a.
72.0 ft × 40.5 ft
b.
40.5 ft × 24.5 ft
c.
40.5 ft × 38.5 ft
d.
24.5 ft × 56.0 ft


Solution:

Let x be the edge length of the square garden.


If the dimensions of the square garden are x × x, then the dimensions of the rectangular garden are (x + a) ft × (x - b) ft.
That is (x + 9) ft × (x - 7) ft

Square garden area = x2 ft2

Area of the rectangular garden = (x + 9)(x - 7) ft2

If the areas of 2 gardens are equal, then x2 = (x + 9)(x - 7)

x2 = x2 + 9x - 7x - 63

2x - 63 = 0

x = 31.5

So, the dimensions of the new rectangular garden are 40.5 ft × 24.5 ft.
[Substitute x = 31.5 in (x + 9) and (x - 7).]


Correct answer : (2)
 3.  
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)
 4.  
Solve (a - 1.4)2 = 0.
a.
- 2.8
b.
2.8
c.
- 1.4
d.
1.4


Solution:

(a - 1.4)2 = 0
[Original equation.]

a - 1.4 = 0
[Set repeated factor equal to 0.]

a = 1.4
[Solve for a.]

The solution of the equation (a - 1.4)2 = 0 is 1.4 .


Correct answer : (4)
 5.  
Solve (b - 9)(b - 13)2 = 0.
a.
- 9 and 13
b.
9 and 13
c.
- 9 and - 13
d.
9 and - 13


Solution:

(b - 9)(b - 13)2 = 0
[Original equation.]

b - 9 = 0 or b - 13 = 0
[Equate each factor to zero.]

b = 9 or b = 13
[Solve for b.]

The solutions of the equation (b - 9)(b - 13)2 = 0 are 9 and 13.


Correct answer : (2)
 6.  
Solve (9x - 20.7)(3x + 10.8)2 = 0.
a.
20.7 and - 10.8
b.
22.7 and 3.6
c.
2.3 and 13.8
d.
2.3 and - 3.6


Solution:

(9x - 20.7)(3x + 10.8)2 = 0
[Original equation.]

9x - 20.7 = 0 or 3x + 10.8 = 0
[Equate each factor to zero.]

x = 2.3 or x = - 3.6
[Solve for x.]

The solutions of the equation (9x - 20.7)(3x + 10.8)2 = 0 are 2.3 and - 3.6 .


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


Solution:

(y - 12)(y + 5) = 0
[Original equation.]

(y - 12) = 0 or (y + 5) = 0
[Equate each factor to zero.]

y = 12 or y = - 5
[Solve for y.]

The solutions of the equation (y - 12)(y + 5) = 0 are 12 and - 5.


Correct answer : (4)
 8.  
Solve (u - 34)(5u + 8)(15u - 7) = 0.
a.
34, 8 5 and 7
b.
34, - 8 5 and 35
c.
- 34, 8 5 and 7
d.
34, 3 and - 35


Solution:

(u - 34)(5u + 8)(15u - 7) = 0
[Original equation.]

(u - 34) = 0 or (5u + 8) = 0 or (15u - 7) = 0
[Equate each factor to zero.]

u = 34 or u = - 8 / 5 or u = 35
[Solve for u.]

The solutions of the equation (u - 34)(5u + 8)(15u - 7) = 0 are 34, - 8 / 5 and 35.


Correct answer : (2)
 9.  
Solve the equation (a - 4)(a + 4) = 0.
a.
- 4 and 0
b.
4 and - 4
c.
4 and 4
d.
- 4 and - 4


Solution:

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

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

a = 4 or a = - 4
[Solve for a.]

The solutions for the equation (a - 4)(a + 4) = 0 are 4 and - 4.


Correct answer : (2)
 10.  
Solve:
f(f + 2) = 0
a.
0 and - 2
b.
4 and - 4
c.
0 and 2
d.
2 and - 2


Solution:

f (f + 2) = 0
[Original equation.]

f = 0 or (f + 2) = 0
[Equate each factor to zero.]

f = 0 or f = - 2
[Simplify.]

The solutions of the equation f(f + 2) = 0 are 0 and - 2.


Correct answer : (1)

*AP and SAT are registered trademarks of the College Board.