Quantitative Aptitude Ques 395

Question: $ {{(a^{2}+2a)}^{2}}+12,(a^{2}+2a)-45 $ can be expressed as

Options:

A) $ (a-1)(a-3)(a^{2}+2a+15) $

B) $ (a-1)(a+3)(a^{2}+2a+15) $

C) $ (a+1)(a+3)(a^{2}+2a+15) $

D) $ (a+1)(a-3)(a^{2}+2a+15) $

Show Answer

Answer:

Correct Answer: B

Solution:

  • Given, $ {{(a^{2}+2a)}^{2}}+12,(a^{2}+2a)-45 $ Let $ (a^{2}+2a)=x $ Then, $ x^{2}+12x-45=x^{2}+15x-3x-45 $ $ =x,(x+15)-3,(x+15) $ $ =(x+15)(x-3) $ Now, putting the value of x in these factors. $ =(a^{2}+2a+15)(a^{2}+2a-3) $ $ =(a^{2}+3a-a-3)(a^{2}+2a+15) $ $ =[a,(a+3)-1,(a+3)(a^{2}+2a+15) $ $ =(a-1)(a+3)(a^{2}+2a+15) $
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