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)  x³y² + 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 :

x³y² + 6x²y² + 8xy² + 48y² :

=  (x³y² + 6x²y²) + (8xy² + 48y²)

=  x²y²(x + 6) + 8y²(x + 6)

=  (x + 6)(x²y² + 8y²)

=  (x²y² + 8y²)(x + 6)

=  y²(x² + 8)(x + 6)

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.