Question

If (x⁶⁰ + 60) is divided by (x + 1), the remainder is

(a) 0
(b) 59
(c) 61
(d) 2

Answer 1

(c) 61

Let:
$p\left(x\right)=x^{60}+60$
$x+1=0\Rightarrow x=-1$
By the remainder theorem, we know that when $p\left(x\right)\text{is divided by}\left(x+1\right),\text{the remainder is}p\left(-1\right).$
Now, we have:
$$\begin{gathered} p\left(-1\right)={\left(-1\right)}^{60}+60 \\ =1+60 \\ =61 \end{gathered}$$