SSC Sample Paper Mock Test-2 SSC CGL Tear-II Paper-1

What is the HCF of the polynomials\[{{x}^{3}}+8,{{x}^{2}}+5x+6\]and \[{{x}^{3}}+2{{x}^{2}}+4x+8?\]

A) \[x+2\]

B) \[x+3\]

C) \[{{(x+2)}^{2}}\]

D) None of these

Correct Answer: A

Solution :

Let \[f(x)={{x}^{3}}+8={{x}^{3}}+{{2}^{3}}=(x+2)({{x}^{2}}-2x+4)\]

\[=(x+2){{(x-2)}^{2}}=(x+2)(x-2)(x-2)\]

\[g\,\,(x)={{x}^{2}}+5x+6={{x}^{2}}+3x+2x+6\]

\[=x\,\,(x+3)+2\,\,(x+3)=(x+3)(x+2)\]

and\[h\,\,(x)={{x}^{3}}+2{{x}^{2}}4x+8={{x}^{2}}(x+2)+4\,\,(x+2)\]

\[=(x+2)({{x}^{2}}+4)\]

\[\therefore \]HCF of \[\{f\,\,(x),g\,\,(x),h\,\,(x)\}=(x+2)\]