Question
When $p(x) = x^3 - 3x^2 + 4x + 32$ is divided by $(x + a),$ the remainder is:
✓
Answer
$x + 2 = 0 $
$\Rightarrow x = -2$
By the remainder theorem, we know that when $p(x)$ is divided by $(x + 2),$ the remainder is $p(-2).$
Now, we have:
$p(-2) = (-2)^3 - 3 \times (-2)^2 + 4 \times (-2) + 32$
$= -8 - 12 - 8 + 32$
$= 4$
$\Rightarrow x = -2$
By the remainder theorem, we know that when $p(x)$ is divided by $(x + 2),$ the remainder is $p(-2).$
Now, we have:
$p(-2) = (-2)^3 - 3 \times (-2)^2 + 4 \times (-2) + 32$
$= -8 - 12 - 8 + 32$
$= 4$
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