The expression x3 q2 ndash x3pt 4x2pt ndash 4x2 q2 3xq2 ndash 3xpt is divisible by ........

Quantitative Aptitude (CDS) Algebra

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The expression x³ q² – x³pt+ 4x²pt – 4x² q²+ 3xq² – 3xpt is divisible by

(x – 1) only

(x – 3) only

both (x – 1) and (x– 3)

neither (x – 1) nor (x – 3)

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Explanation:

x³ q² – x³pt +4x²pt – 4x² q²+ 3xq² – 3xpt
If we put x = 1
= q² – pt + 4pt – 4q² + 3q² – 3pt = 0
So, (x –1) is a factor of this function of we put x =3 Checking x = 3 also,
= 27q² – 27pt + 36pt – 36q² + 9q² – 9pt = 0
So, (x – 1) and (x – 3) both are factors.