PRACTICE QUESTIONS ON FACTORING POLYNOMIALS

Factoring the following monomials

Questions :

1)  25n2

2)  18xy

3)  12y

4)  21y2

5)  81a

6)  92q

7)  36x3

8)  24h

9)  48x2

10)  x2y3

Answers :

1)  ⋅ 5 ⋅ n ⋅ n

2)  ⋅ 3 ⋅ 3 ⋅ x ⋅ y

3)  ⋅ 2 ⋅ 3 ⋅ y

4)  ⋅ 7 ⋅ y ⋅ y

5)  ⋅ 3 ⋅ 3 ⋅ 3 ⋅ a

6)  ⋅ 2 ⋅ 23 ⋅ q

7)  2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ x ⋅ x ⋅ x

8)  2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ h

9)  2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ x ⋅ x

10)   x ⋅ x ⋅ y ⋅ y ⋅ y

Solution

Factoring the following binomials

Questions :

1)  4x + 24y

2)  2x2 – 8x

3)  x2 – 3x

4)  4x2y3 + 6x3y2

5)  9m2 - 16n2

6)  a2b2 - c2d2

7)  x4 - y4

8)  3(x – 6) + d(x – 6)

Solution

9)  4x + 8

10)  5x2 - 15x

Solution

Answers :

1)  4(x + 6y)

2)  2x(x - 4)

3)  x(x - 3)

4)  2xy(2x + 3y)

5)  (3m + 4n)(3m - 4n)

6)  (ab + cd)(ab - cd)

7)  (x2 + y2)(x + y)(x - y)

8)  (x – 6)(3 + d)


9)  4(x + 2)

10)  5x(x - 3)

Factoring the following trinomials

Questions :

1)  3a + 6ab + 9a2

2)  ab + bc - 2b

3)  2x(x + 4) + 3x + 12

4)  x2 + 5x + 6

5)  x2 - 15x + 56

6)  x2 + 2x - 15

7)  x2 - x - 20

8)  2x2 + 9x + 9

9)  3x2 + x - 4

10)  x2 + 8x + 16

11)  x2 + 6xy + 9y2

12)  4a2 - 20ab + 25b2

13)  16a + 64b - 4c

Answers :

1)  3a(1 + 2b + 3a)

2)  b(a + c – 2)

3)  (x + 4)(2x + 3)

4)  (x + 2)(x + 3)

5)  (x - 7)(x - 8)

6)   (x - 3)(x + 5)

7)  (x - 5)(x + 4)

8)  (2x + 3)(x + 3)

9)  (x - 1)(3x + 4)

10)  (x + 4)(x + 4)

11)  (x + 3y)(x + 3y)

12)  (2a - 5b)(2a - 5b)

13)  4(4a + 16b - c) 

Solution

Factoring the following expressions with four terms

Questions :

1)  x2 + 4x – 5x - 20

2)  x2 - 7x + 3x - 21

3)  x2 - 3x + 2x - 6

4)  x2 - 6x - 3x + 18

5)  x2 + 7x - 9x - 63

6)  2x2 + x - 6x - 3

7)  3x2 + 2x - 12x - 8

8)  4x2 - 3x - 8x + 6

9)  9x2 + 4x - 9x - 4

Solution

10)  x3 + 3x2 + 6x + 18

11)  x3 + 2x2 - 9x - 18

Solution

Answers :

1)  (x + 4) (x – 5)

2)  (x - 7) (x + 3)

3)  (x - 3) (x + 2)

4)  (x - 6) (x - 3)

5)  (x + 7) (x - 9)

6)  (2x + 1) (x - 3)

7)  (3x + 2) (x - 4)

8)  (4x - 3) (x - 2)

9)   (9x + 4) (x - 1)


10)  (x + 3)(x2 + 6)

11)  (x + 2)(x + 3)(x - 3)

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