FACTORING BY GROUPING WORKSHEET

Factor each polynomial :

1)  ax + bx + ay + by 

2)  x2 + xt + ax + at

3)  2y3 + 4y2 + y + 2

4)  xy - 5y - 2x + 10

5)  6ax + 3bd - 2ad - 9bx

6)  3x3 + 3x2 - 6x - 6

7)  2ax2 - cx2 + 6a - 3c

8)  4a2 + 5ab - 10b - 8a

9)  a2x + 3a2y - 9x - 27y

10)  x3y+ 6x2y2 + 8xy2 + 48y2

Detailed Answer Key

1. Answer : 

ax + bx + ay + by  =  (ax + bx) + (ay + by)

=  x(a + b) + y(a + b) 

=  (x + y)(a + b)

2. Answer :

x2 + xt + ax + at  =  (x2 + xt) + (ax + at)

=  x(x + t) + a(x + t)

=  (x + t)(x + a)

3. Answer :

2y3 + 4y2 + y + 2  =  (2y3 + 4y2) + (y + 2)

=  2y2(y + 2) + 1(y + 2)

=  (y + 2)(2y2 + 1)

4. Answer :

xy - 5y - 2x + 10  =  (xy - 5y) + (-2x + 10)

=  y(x - 5) - 2(x - 5)

=  (x - 5)(y - 2)

5. Answer :

6ax + 3bd - 2ad - 9bx  =  6ax - 9bx - 2ad + 3bd

=  (6ax - 9bx) + (-2ad + 3bd)

=  3x(2a - 3b) - d(2a - 3b)

=  (2a - 3b)(3x - d)

6. Answer :

3x3 + 3x2 - 6x - 6  =  (3x3 + 3x2) + (-6x - 6)

=  3x2(x + 1) - 6(x + 1)

=  (x + 1)(3x2 - 6)

=  (3x2 - 6)(x + 1)

=  3(x2 - 2)(x + 1)

7. Answer :

2ax2 - cx2 + 6a - 3c  =  (2ax2 - cx2) + (6a - 3c)

=  x2(2a - c) + 3(2a - c)

=  (2a - c)(x2 + 3)

8. Answer :

4a2 + 5ab - 10b - 8a  =  4a2 + 5ab - 8a - 10b

=  (4a2 + 5ab) + (-8a - 10b)

=  a(4a + 5b) - 2(4a + 5b)

=   (4a + 5b)(a - 2)

9. Answer :

a2x + 3a2y - 9x - 27y  =  (a2x + 3a2y) + (-9x - 27y)

=  a2(x + 3y) - 9(x + 3y)

=  (x + 3y)(a2 - 9)

=  (x + 3y)(a2 - 32)

=  (x + 3y)(a + 3)(a - 3)

10. Answer :

x3y+ 6x2y2 + 8xy2 + 48y2 :

=  (x3y+ 6x2y2) + (8xy2 + 48y2)

=  x2y2(x + 6) + 8y2(x + 6)

=  (x + 6)(x2y2 + 8y2)

=  (x2y2 + 8y2)(x + 6)

=  y2(x2 + 8)(x + 6)

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