SSC Sample Paper Mock Test-11 SSC CGL Tear-II Paper-1

The HCF of two polynomials is a + 5 and their LCM is \[(a+5)(a+4)(a-1).\] If one of the polynomial is \[{{a}^{2}}+4\,\,a-5,\] then the other polynomial is

A) \[{{a}^{2}}+9a-20\]

B) \[{{a}^{2}}-9a+20\]

C) \[{{a}^{2}}+9a+20\]

D) \[{{a}^{2}}-9a-20\]

Correct Answer: C

Solution :

As we know,

\[HCF\times LCM=\]Product of polynomials

Let other polynomial be q(x).

\[p\,\,(x)=({{a}^{2}}+4a-5)\]

\[\therefore \]\[(a+5)(a+5)(a+4)(a-1)=({{a}^{2}}+4a-5)\,\,q\,\,(x)\]

\[q\,\,(x)=(a+5)(a+5)\times \frac{(a+4)(a-1)}{(a+5)(a-1)}\]

\[q\,\,(x)=(a+5)(a+4)={{a}^{2}}+9a+20\]