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Simplifying Polynomials Worksheet - Page 2

Simplifying Polynomials Worksheet
  • Page 2
 11.  
Find GCF of a4, 24a2, 12a.
a.
a
b.
12
c.
12a
d.
a2


Solution:

a4 = a × a × a × a
[Write the factors of a4.]

24a2 = 12 × 2 × a × a
[Write the factors of 24a2.]

12a = 12 × a
[Write the factors of 12a.]

The GCF of two or more numbers is the product of their common factors.

The GCF of a4, 24a2 and 12a is: a


Correct answer : (1)
 12.  
Factor x3 - 3x2 + 2x completely.
a.
x(x - 2)(x + 1)
b.
x(x - 2)(x - 1)
c.
x(x + 2)(x - 1)
d.
None of the above


Solution:

x3 - 3x2 + 2x
[Original expression.]

The GCF of x3, 3x2 and 2x is x.

= x(x2 - 3x + 2)
[Use GCF to factor.]

= x(x - 2)(x - 1)
[Factor the trinomial.]


Correct answer : (2)
 13.  
Factor 2x3 + 4x2 - 16x completely.
a.
2x(x - 4)(x - 2)
b.
2x(x + 4)(x - 2)
c.
2x(x + 4)(x + 2)
d.
None of the above


Solution:

2x3 + 4x2 - 16x
[Original expression.]

= 2x(x2 + 2x - 8)
[Use GCF to factor.]

= 2x(x + 4)(x - 2)
[Factor the trinomial.]


Correct answer : (2)
 14.  
Factor 3x3 + 9x2 + 54x completely.
a.
-3x(x + 6)(x + 3)
b.
-3x(x - 6)(x + 3)
c.
-3x(x - 6)(x - 3)
d.
None of the above


Solution:

-3x3 + 9x2 + 54x
[Original expression.]

= -3x(x2 - 3x - 18)
[Use GCF to factor.]

= -3x(x - 6)(x + 3)
[Factor the trinomial.]


Correct answer : (2)
 15.  
Factor - 3x3 + 9x2 + 30x completely.
a.
-3x(x - 5)(x - 2)
b.
-3x(x + 5)(x - 2)
c.
-3x(x - 5)(x + 2)
d.
None of the above


Solution:

-3x3 + 9x2 + 30x
[Original expression.]

= -3x(x2 - 3x - 10)
[Factor out the GCF.]

The factors are 2 and -5
[2 + (-5) = -3 and 2 x (-5) = -10]

= -3x(x - 5)(x + 2)
[Factorize.]


Correct answer : (3)
 16.  
Factor - 2x2 - 6x + 36 completely.
a.
-2(x - 6)(x - 3)
b.
-2(x + 6)(x - 3)
c.
-2(x + 6)(x + 3)
d.
None of the above


Solution:

-2x2 - 6x + 36
[Original expression.]

= -2(x2 + 3x - 18)
[Use GCF to factor.]

= -2(x + 6)(x - 3)
[Factor the trinomial.]


Correct answer : (2)
 17.  
Factor 3x3 - 9x2 - 54x completely.
a.
3x(x + 6)(x + 3)
b.
3x(x - 6)(x + 3)
c.
3x(x - 6)(x - 3)
d.
None of the above


Solution:

3x3 - 9x2 - 54x
[Original expression.]

= 3x(x2 - 3x - 18)
[Use GCF to factor.]

= 3x (x - 6) (x + 3)
[Factor the trinomial.]


Correct answer : (2)
 18.  
Factor: - 6x3 + 3x2 + 54x - 27
a.
(-6x + 3)(x - 3)(x - 3)
b.
(-6x - 3)(x + 3)(x - 3)
c.
(-6x + 3)(x + 3)(x - 3)
d.
None of the above


Solution:

-6x3 + 3x2 + 54x - 27
[Original expression.]

= (-6x3 + 3x2) + (54x - 27)
[Group terms.]

= x2(-6x + 3) - 9(-6x + 3)
[Factor each group.]

= (-6x + 3) (x2 - 9)
[Use distributive property.]

= (-6x + 3)(x + 3)(x - 3)
[Use the formula a2 - b2 = (a + b)(a - b).]


Correct answer : (3)
 19.  
Factor: - 5x3 - 6x2 + 20x + 24
a.
(-5x - 6)(x - 2)(x - 2)
b.
(-5x + 6)(x + 2)(x - 2)
c.
(-5x - 6)(x + 2)(x - 2)
d.
None of the above


Solution:

-5x3 - 6x2 + 20x + 24
[Original expression.]

= (-5x3 - 6x2) + (20x + 24)
[Group terms.]

= -x2(5x + 6) + 4(5x + 6)
[Factor each group.]

= (-5x - 6) (x2 - 4)
[Use distributive property.]

= (-5x - 6) (x + 2)(x - 2)
[Use the formula a2 - b2 = (a + b)(a - b).]


Correct answer : (3)
 20.  
Factor: 4x3 - 7x2 + 4x - 7
a.
None of the above
b.
(4x - 7)(x2 - 1)
c.
(4x - 7)(x2 + 1)
d.
(4x + 7)(x2 + 1)


Solution:

4x3 - 7x2 + 4x - 7
[Original expression.]

= (4x3 - 7x2) + (4x - 7)
[Group terms.]

= x2(4x - 7) + 1(4x - 7)
[Factor each group.]

= (4x - 7)(x2 + 1)
[Use distributive property.]


Correct answer : (3)

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