MCQ
When $p(x) = x^3 - ax^2 + x$ is divided by $(x - a),$ the remainder is:
- A$0$
- ✓$a$
- C$2a$
- D$3a$
✓
Answer
Correct option: B.
$a$
$p(x) = x^3 - ax^2 + x$
$x - a = 0 ⇒ x = a$
By the remainder theorem, we know that when $p(x)$ is divided by $(x - a)$, the remainder is $p(a).$
Now, $p(a) = a^3 - ax^2 + a$
$= a^3 - a^3 + a$
$= a$
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