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Factoring by GCF Worksheet - Page 3

Factoring by GCF Worksheet
  • Page 3
 21.  
Factor:
x9c + 15 - 64y6d
a.
(x3c + 5 - 4y2d) [x6c + 10 + 4x3c - 5y2d - 16y4d]
b.
(x3c + 5 + 4y2d) [x6c + 10 + 4x3c - 5y2d - 16y4d]
c.
(x3c + 5 + 4y2d) [x6c + 10 + 4x3c + 5y2d + 16y4d]
d.
(x3c + 5 - 4y2d) [x6c + 10 + 4x3c + 5y2d + 16y4d]


Solution:

x9c + 15 - 64y6d

= x3(3c + 5) - 64y3(2d)

= (x3c + 5)3 - (4y2d)3
[Use power property amn = (am)n .]

= (x3c + 5 - 4y2d) [(x3c + 5)2 + 4x3c + 5y2d + (4y2d)2]
[a3 - b3 = (a - b) (a2 + ab + b2).]

= (x3c + 5 - 4y2d) [x6c + 10 + 4x3c + 5y2d + 16y4d]


Correct answer : (4)
 22.  
If the area of a square board is (81z2 + 144z + 64) cm2, then find the length of its side.
a.
(9z + 8) cm
b.
(10z + 8) cm
c.
(9z - 8) cm
d.
(9z + 9) cm


Solution:

Area of the square board = 81z2 + 144z + 64

= (9z)2 + 2(9z) (8) + (8)2

= (9z + 8)2
[Use the formula: a² + 2ab + b² = (a + b)2.]

Area of the square board = (length)2

(length)2 = (9z + 8)2

So, the length is (9z + 8) cm.


Correct answer : (1)
 23.  
Express the volume 27x3 - 64 of box in factored form.
a.
(3x - 4) (9x2 - 12x + 16)
b.
(3x + 4) (9x2 + 12x + 16)
c.
(3x - 4) (9x2 + 12x - 16)
d.
(3x - 4) (9x2 + 12x + 16)


Solution:

Volume of the box = 27x3 - 64

= (3x)3 - (4)3

= (3x - 4)((3x)2 + (3x)(4) + (4)2)
[Use the formula: a³ - b³ = (a - b) (a2 + ab + b2).]

= (3x - 4)(9x2 + 12x + 16)
[Simplify.]


Correct answer : (4)
 24.  
Factor 3an + 9 + 4an + 4, assume all exponents are positive integers.
a.
an + 4[3a5 + 4]
b.
an + 4[3a5 + 3]
c.
an - 4[3a5 - 4]
d.
an - 4[3a5 + 4]


Solution:

3an + 9 + 4an + 4

= 3an + 4 + 5 + 4an + 4

= 3an + 4 · a5 + 4an + 4
[Use exponent property am + n = am. an.]

= an + 4[3a5 + 4]


Correct answer : (1)
 25.  
Factor:
x6a y6b + 2x3a y3bz4a + z8a
a.
(xa y3b + z4a)2
b.
(x3ay3b + z4a)2
c.
2x9ay9bz12a
d.
x3a - z4a


Solution:

x6a y6b + 2x3a y3b z4a + z8a

= (x3a y3b)2 + 2 (x3a y3b) (z4a) + (z4a)2
[a = x3a y3b, b = z4a.]

= (x3ay3b + z4a)2
[(a + b)2.]


Correct answer : (2)
 26.  
A circle of radius 722 is to be cut from a square paper of side x. Express the area of the remaining portion in a factored form. [Take π = 22 7.]
a.
(x + 1)(x - 1)
b.
x2 + 1
c.
(x - 10)2
d.
(x + 10)2


Solution:

Area of the remaining portion = Area of the square - Area of the circle

Area of the square = x2

Area of the circle = πr2 = 227(722)2 = 1
[Simplify.]

Area of the remaining portion = x2 - 1
[a = x, b = 1.]

= (x + 1)(x - 1)
[a2 - b2 = (a + b) (a - b).]


Correct answer : (1)
 27.  
A small square piece of side y is removed from a square cloth of side x as shown. What is the area of the remaining portion?

a.
x2 + y2
b.
(x + y)2
c.
(x - y)2
d.
(x + y)(x - y)


Solution:

Area of big square cloth = x2

Area of removed cloth = y2

Area of the remaining cloth = x2 - y2

= (x + y)(x - y)
[a2 - b2 = (a + b)(a - b).]


Correct answer : (4)

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