PRACTICE QUESTIONS ON FACTORIZATION

Part A

Factories the following monomials

(1)  25n2

(2)  18xy

(3)  12y

(4)  21y2

(5)  81a

(6)  92q

(7)  36x3

(8)  24h

(9)  48x2

(10)  x2y3

Solution

Answers :

(1)  5 ⋅ 5 ⋅ n ⋅ n

(2)  2 ⋅ 3 ⋅ 3 ⋅ x ⋅ y

(3)  2 ⋅ 2 ⋅ 3 ⋅ y

(4)  ⋅ 7 ⋅ y ⋅ y

(5)  ⋅ 3 ⋅ 3 ⋅ 3 ⋅ a

(6)  2 ⋅ 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

Part B

Factor the following polynomials by grouping

(1)  x2 + xt + ax + at

(2)  2y3 + 4y2 + y + 2

(3)  xy - 5y - 2x + 10

(4)  6ax+3bd-2ad-9bx

(5)  3x3 + 3x2 - 6x - 6

(6)  2ax2 - cx2 + 6a - 3c

(7)  4a2 + 5ab - 10b - 8a

(8)  a2x + 3a2y - 9x - 27y

Solution

Answers :

(1)  (x + t)(x + a)

(2)  (y + 2)(2y2 + 1)

(3)  (x - 5)(y - 2)

(4)  (2a - 3b)(3x - d)

(5)  3(x2 - 2)(x + 1)

(6)  (2a - c)(x2 + 3)

(7)  (4a + 5b)(a - 2)

(8)  (x + 3y)(a + 3)(a - 3)

Part C

Factor the following polynomials using algebraic identities

(1)  x2 + 6xy + 9y2

(2)  4a2 - 20ab + 25b2

(3)  2x2 + 12xy + 18y2

(4)  2ab2 - 16ab + 32a

(5)  x2 - 25y2

(6)  9m2 - 16n2

(7)  x4 - y4

(8)  8p4 - 18q4

Solution

Answers :

(1)  (x+3y)(x+3y)

(2)  (2a-5b)(2a-5b)

(3)  2(x+3y)(x+3y)

(4)  2a(b-4)2

(5)  (x+5y)(x-5y)

(6)  (3m+4n)(3m-4n)

(7)  (x2+y2)(x+y)(x-y)

(8)  2(4p2+9q2)(2p+3q)(2p-3q)

Part D

Factoring linear expression

(1)  4x + 8

(2)  16a + 64b - 4c

(3)  36x - 16

(4)  35 + 21a

(5)  4a - 8b + 5ax - 10bx

Answers :

(1)  4(x + 2)

(2)  4(4a + 16b - c)

(3)  4(9x - 4)

(4)  7(5 + 3a)

(5)  (a - 2b) (4 + 5x)

Part E

Factoring quadratic polynomial

(1)  x2 + 6x + 5

(2)  x2 + 2x - 35

(3)  x2 - 6x - 7

(4)  x2 - 18x + 65

(5)  3x2 – 5x – 12

(6)  2x2 + x - 6

Solution

Answers :

(1)  (x + 1)(x + 5)

(2)  (x - 5)(x + 7)

(3)  (x - 7)(x + 1)

(4)  (x - 5)(x - 13)

(5)  (3x + 4)(x - 3)

(6)  (x + 2)(2x - 3)

Part F

Factor sum of difference of the cubes :

(1)  m3 + 8

(2)  a3 - 125

(3)  x3 + 8y3

(4)  8x3 - 125y3

(5)  27x3 + 64y3

(6)  2m3 - 54n3

Solution

Answers :

(1)   (m + 2)(m2 - 2m + 4)

(2)  (a - 5)(a2 + 5a + 25)

(3)  (x + 2y)(x2 - 2xy + 4y2)

(4)  (2x - 5y)(4x2 + 10xy + 25y2)

(5)  (3x + 4y)(9x2 - 12xy + 16y2)

(6)  2(m - 3n)(m2 + 3mn + 9n2)

Part G

Factor the following cubic polynomial 

(1)  x3 - 2x2 - 5 x + 6

(2)  4x3 - 7x + 3

(3)  x3-23x2+142x-120

(4)  4x3-5x2+7x-6

(5)  x3 - 7x + 6

(6)   x3 +13x2+32x+20

Solution

(1)  (x-1) (x-3) (x+2)

(2)  (x-1)(2x-1)(2x+3)

(3)  (x-1)(x-10)(x-12)

(4)  (x-1)(4x2-x+6).

(5)  (x-1)(x+3)(x-2)

(6)  (x+1)(x+10)(x+2)

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