question_answer

When \[16{{x}^{4}}+12{{x}^{3}}-10{{x}^{2}}+8x+20\] is divided by \[4x-3,\] the quotient and the remainder are, respectively

A)  \[4{{x}^{3}}+6{{x}^{2}}+2x\] and \[\frac{61}{2}\]

B)  \[4{{x}^{3}}+6{{x}^{2}}+\frac{7}{2}\] and \[\frac{51}{2}\]

C)  \[6{{x}^{2}}+2x+\frac{2}{7}\] and \[\frac{61}{2}\]

D)  \[4{{x}^{3}}+6{{x}^{2}}+2x+\frac{7}{2}\]

Correct Answer: D

Solution :

Ans.                                \[\therefore \]    Remainder \[=\frac{61}{2}\]