Factoring Using the Distributive Property Worksheet

Factoring Using the Distributive Property Worksheet
  • Page 1
 1.  
Solve the equation.
4x4 - 36x2 = 0
a.
3, 6
b.
0, 4, 9
c.
0, 3, 9
d.
0, 3, -3


Solution:

4x4 – 36x2 = 0
[Given equation.]

4x2(x2 – 9) = 0
[Factor out GCF.]

4x2(x2 – 32) = 0

4x2(x – 3)(x + 3) = 0
[Factor difference of squares.]

x = 0, 3, - 3
[By setting each variable factor equal to zero, you can find the solution for x.]


Correct answer : (4)
 2.  
Factor the GCF out of 9x4 + 18x.
a.
9x(x3 + 3)
b.
9x(x3 + 2)
c.
3x(x3 + 6x)
d.
3x2(x + 6)


Solution:

9x4 + 18x
[Given expression.]

9x4 = 3 · 3 · x · x · x · x
[Factor.]

18x = 3 · 3 · 2 · x
[Factor.]

The GCF = 3 · 3 · x = 9x
[It is the product of all the common factors.]

9x4 + 18x = 9x(x3 + 2)
[Use the distributive property to factor the greatest common factor out of the polynomial.]


Correct answer : (2)
 3.  
Factor the GCF out of 20t5 + 5t3.
a.
5t2(4t3 + 1)
b.
4t2(5t3 + 4)
c.
5t3(4t2 + 1)
d.
4t3(5t2 + 4)


Solution:

20t5 + 5t3
[Given expression.]

20t5 = 5 · 4 · t · t · t · t · t
[Factor.]

5t3 = 5 · t · t · t
[Factor.]

The GCF is 5t3.
[It is the product of all the common factors.]

20t5 + 5t3 = 5t3(4t2 + 1)
[Use the distributive property to factor the greatest common factor out of the polynomial.]


Correct answer : (3)
 4.  
Factor the GCF out of 6a5 + 12a3 - 3a2.
a.
3a2(2a3 + 4a - 1)
b.
3a2(2a3 + 4a + 1)
c.
3a2(2a3 - 4a - 1)
d.
3a2(2a3 + 4a - a)


Solution:

6a5 + 12a3 - 3a2
[Given expression.]

6a5 = 3(2)(a2)(a3)
[Factor.]

12a3 = 3(4)(a2)(a)
[Factor.]

3a2 = 3(a2)
[Factor.]

GCF = 3a2
[It is the product of all the common factors.]

6a5 + 12a3 - 3a2 = 3a2(2a3 + 4a - 1)
[Use the distributive property to factor the greatest common factor out of the polynomial.]


Correct answer : (1)
 5.  
Factor the GCF out of 16d6 - 4d2 + 2d.
a.
2d(8d5 - 2d - 1)
b.
2d(8d5 - 2d + 1)
c.
2(8d5 - 2d + 1)
d.
2d(8d5 - 2d + d)


Solution:

16d6 - 4d2 + 2d
[Given expression.]

16d6 = 2 × 8 × d × d2 × d3
[Factor.]

4d2 = 2 × 2 × d × d
[Factor.]

2d = 2 × d
[Factor.]

The GCF = 2d.
[It is the product of all the common factors.]

16d6 - 4d2 + 2d = 2d(8d5 - 2d + 1)
[Use the distributive property to factor the greatest common factor out of the polynomial.]


Correct answer : (2)
 6.  
Factor the expression completely.
25x3 + 10x2
a.
5x2(5x + x)
b.
5x2(5x2 + 1)
c.
5x2(5x + 2)
d.
5x2(5x - 2)


Solution:

25x3 + 10x2
[Given expression.]

25x3 = 5 × 5 × x2 × x
[Factor.]

10x2 = 5 × 2 × x2
[Factor.]

25x3 + 10x2 = 5x2(5x + 2)
[GCF = 5x2.]

This polynomial is factored completely. Because 5x + 2 cannot be factored using integer co-efficient.


Correct answer : (3)
 7.  
Factor the expression completely.
- 4w4 + 28w3
a.
4w3(w - 7)
b.
- 4w3(w + 7)
c.
- 4w3(w - 7)
d.
- 4w3(w - 1)


Solution:

- 4w4 + 28w3
[Given expression.]

4w4 = 4 × w3 × w
[Factor.]

28w3 = 4 × 7 × w3
[Factor.]

- 4w4 + 28w3 = - 4 × w3 × w + 4 × 7 × w3

= - 4w3(w - 7)
[Take the common factor out.]


Correct answer : (3)
 8.  
Factor the expression completely.
3d4 + 3d3 - 60d2
a.
3d2(d - 4)(d + 5)
b.
3d2(d - 4)(d - 5)
c.
3d2(d + 4)(d + 5)
d.
3d2(d + 4)(d -5)


Solution:

3d4 + 3d3 - 60d2
[Given.]

3d4 = 3 × d2 × d2
[Factor.]

3d3 = 3 × d2 × d
[Factor.]

60d2 = 3 × 20 × d2
[Factor.]

The GCF is 3d2.

3d4 + 3d3 - 60d2 = 3d2(d2 + d - 20)
[Factor out GCF.]

= 3d2(d - 4)(d + 5)
[Factor the trinomial.]


Correct answer : (1)
 9.  
Factor the expression completely.
- 27z4 + 3z2
a.
- 3z2(3z - 1)2
b.
- 3z2(3z + 1)2
c.
3z2(3z - 1)(3z + 1)
d.
- 3z2(3z - 1)(3z + 1)


Solution:

- 27z4 + 3z2
[Given.]

27z4 = 3 × 9 × z2 × z2
[Factor.]

3z2 = 3 × z2
[Factor.]

The GCF is 3z2.

- 27z4 + 3z2 = - 3z2(9z2 - 1)
[Factor out GCF.]

= - 3z2(3z + 1)(3z - 1)
[Use (a2 - b2) = (a + b)(a - b).]


Correct answer : (4)
 10.  
Factor the expression completely x4 + x3 - 16x -16.
a.
(x3 + 16)(x - 1)
b.
(x3 + 16)(x + 1)
c.
(x3 - 1)(x + 16)
d.
(x3 - 16)(x + 1)


Solution:

x4 + x3 -16x -16
[Given.]

= (x4 + x3) - (16x + 16)
[Group terms.]

= x3(x + 1) - 16(x + 1)
[Factor each group.]

= (x3 - 16)(x + 1)
[Use distributive property.]

Therefore, x4 + x3 - 16x - 16 = (x3 - 16)(x + 1)


Correct answer : (4)

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