Question

The remainder obtained when ($x^4+4x^3+2$) is divided by ($x+1$) = .

• A. 10
• B. -10
• C. -1
• D. 1

Answer 1

The correct option is C -1

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 ($x+1)$,
$\Rightarrow$ a = -1.
$\therefore$ f(-1) = $(-1{)}^4+4\times (-1{)}^3+2$ = -1
Hence, remainder = -1