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Polynomials — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSPolynomials1 Mark
Question
When $p(x) = x^3 + ax^2 + 2x + a$ is divided by $x + a,$ the remainder is:
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Answer

$x + a = 0$
$\Rightarrow x = -a$
By the remainder theorem, we know that when $p(x)$ is divided by $(x + a),$ the remainder is $p (-a).$
Thus, we have: $P(-a) = (-a)^3 + a \times (-a)^2 + 2 \times (-a) + a$
$= -a^3 + a^3 - 2a + a$
$= -a$

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