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Factoring Polynomials Worksheet

Factoring Polynomials Worksheet
  • Page 1
 1.  
Factor: x3 - 343
a.
x3 - 21x2 + 147x - 343
b.
x3 + 21x2 + 147x + 343
c.
(x - 7)(x2 + 7x + 49)
d.
(x - 7)(x2 - 7x + 49)


Solution:

x3 - 343

= x3 - 73
[Write the terms as the difference between cubes.]

= (x - 7)(x2 + 7x + 49)
[Using (a3 - b3) = (a - b) (a2 + ab + b2).]


Correct answer : (3)
 2.  
Find the value of a that makes ax2 - 20x + 25 a perfect square.
a.
4
b.
2
c.
20
d.
1


Answer: (a)


Correct answer : (1)
 3.  
Find the value of b that makes x2 + bx + 36 a perfect square.
a.
12
b.
24
c.
6
d.
16


Answer: (a)


Correct answer : (1)
 4.  
Express as a perfect square.
y2 + 18y + 81
a.
(y + 11)2
b.
y(y + 9)
c.
(y + 9)2
d.
(y - 9)2


Answer: (c)


Correct answer : (3)
 5.  
Express as a perfect square.
z2q2 + 5zq + 6.25
a.
(zq + 2.7)2
b.
(zq - 2.4)2
c.
(zq + 2.5)2
d.
(zq - 2.5)2


Answer: (c)


Correct answer : (3)
 6.  
Express as a perfect square.
g2 - 8g + 16
a.
(g - 4)2
b.
(g + 5)2
c.
(g + 4)2
d.
(g - 6)2


Answer: (a)


Correct answer : (1)
 7.  
Express as a perfect square.
z2 - 9.2z + 21.16
a.
(z + 4.6)2
b.
(z + 4.8)2
c.
(z - 4.6)2
d.
(z - 4.5)2


Answer: (c)


Correct answer : (3)
 8.  
Express as a perfect square.
k2-16k7+6449
a.
(k -87)2
b.
(k +87)2
c.
(k -18)2
d.
(k +17)2


Answer: (a)


Correct answer : (1)
 9.  
Factor 8dn + 7 + 9dn +2, assume all exponents are positive integers.
a.
dn - 9[8d5+ 9]
b.
dn + 2[8d5 + 9]
c.
dn + 9[8d5 + 9]
d.
dn - 2[8d5 + 9]


Answer: (b)


Correct answer : (2)
 10.  
Factor 3dn +10 + 6dn +5, assume all exponents are positive integers.
a.
dn + 5[2d5+ 5]
b.
dn - 5[2d5 +6]
c.
dn - 5[2d5 + 5]
d.
3dn + 5[d5 + 2]


Answer: (d)


Correct answer : (4)

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