InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Factorize :`64 a^3+125 b^3+240 a^2b+300 a b^2``8/(27)x^3+1+4/3x^2+2x``x^3+8y^3+6x^2y+12 x y^2``8a^3-27 b^3-36 a^2b+54 a b^2``x^3-12 x(x-4)-64` |
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Answer» 1)`64a^3+125b^3+240a^b+300ab^2` `(4a)^3+(5b)^3+3*(4a)^2*(5b)+2*(4a)(5b)^2` `(4a+5b)^3` 2)`8/27*x^3+1+4/3*x^2+2x` `(2/3)^3+1^3+3x(2/33x)^2*1+3(2/3x)*1^2` `(2/3x+1)^3`. |
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| 2. |
Examples based on the middle term concepts : `(i) 4sqrt3 x^2 + 5x - 2sqrt3 (ii) 5sqrt5 x^2 + 30 x + 8sqrt5` |
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Answer» 1)`4sqrt3*2+5x-2sqrt3` `4sqrt3*2+8x-3x-2sqrt3` `4(sqrt3x+1)-sqrt3(sqrt3x+2)` `(4x-sqrt3)(sqrt3x+2)` 2)`5sqrt5*2+30x+8sqrt5` `5sqrt5*x+10x+10x+8sqrt5` `5(sqrt5x+4)+2sqrt5(sqrt5+4)` `(5x+2sqrt5)(sqrt5x+4)`. |
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| 3. |
Factorize:(i) `8x^3+27 y^3+z^3-18 x y z`,(ii) `a^3-8b^3-64 c^3-24 a b c` |
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Answer» 1)`8x^3+27y^3+z^3-18xyz` `(2x+3y+z)(4x^2+9y^2+z^2-6xy-3yz-2xz)` 2)`a^3-8b^3-64c^3-24abc` `(a-2b-4c)(a^2+4b^2+16c^2+2ab+4ac-8bc)`. |
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| 4. |
Factorize : `p^3(q-r)^3+q^3(r-p)^3+r^3(p-q)^3` |
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Answer» `p^3(q-r)^3+q^3(r-p)^3+r^3(p-q)^3` after factorization `3(p(q-r)q(r-p)r(p-q))` `2pqr(q-r)(r-p)(p-q)`. |
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| 5. |
Factorize :`27 a^3+1/(64 b^3)+(27a^2)/(4b)+(9a)/(16 b^2)`` |
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Answer» `(3a)^3+(1/(4b))^3+(3*(3a)^2)/(4b)+(3a)/(4b)^2` `(3a+1/(4b))^3`. |
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