Question

If f(x) = x4+4x3+2 and g(x) = x+2, then the remainder obtained when f(x) is divided by g(x) = .

• A. -14
• B. 14
• C. 12
• D. -12

Answer 1

The correct option is A -14

According to the remainder theorem, the remainder obtained when a polynomial f($x$) is divided by ($x-a$) is f(a).
Given, f($x$) = $x^4+4x^3+2$.
Comparing ($x-a)$ with g($x$) = ($x+2)$,
$\Rightarrow$ a = -2.
$\therefore$ f(-2) = $(-2{)}^4+4\times (-2{)}^3+2$ = -14.
Hence, remainder = -14.