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 |
Answers :
(1) 5 ⋅ 5 ⋅ n ⋅ n (2) 2 ⋅ 3 ⋅ 3 ⋅ x ⋅ y (3) 2 ⋅ 2 ⋅ 3 ⋅ y (4) 3 ⋅ 7 ⋅ y ⋅ y (5) 3 ⋅ 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 |
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 |
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 |
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 |
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
(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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