MCQ
When $p(x) = x^3+a x^2+2 x+a$ is divided by $x + a,$ the remainder is:
- A$1$
- B$0$
- C$a$
- ✓$-a$
✓
Answer
Correct option: D.
$-a$
$x+a=0$
$\Rightarrow x=-a$
By the remainder theorem, we know that when $p(x)$ is divided by $(x+a)$, the remainder is $p(-a)$.
Thus, we have: $P(-a)=(-a)^3+a \times(-a)^2+2 \times(-a)+a$
$=-a^3+a^3-2 a+a$
$=-a$
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