Which of the following is a factor of $x^{3} + 4 x^{2} + 5 x + 6$

x - 3

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x + 2

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x + 3

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x - 2

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Solution

The correct option is A $x + 3$
Let, $p (x) = x^{3} + 4 x^{2} + 5 x + 6$
put $x = - 3$ in $p (x)$
$p (- 3) = (- 3)^{3} + 4 (- 3)^{2} + 5 (- 3) + 6$
$= - 27 + 36 - 15 + 6$
$= - 42 + 42 = 0$
Since, $p (- 3) = 0$
$∴ x + 3$ is a factor of $p (x)$
Option C is correct.

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Similar questions

Which of the following is a polynomial ?

(a) $x^{2} - 5 x + 4 \sqrt{x} + 3$ (b) $x^{\frac{3}{2}} - x + x^{\frac{1}{2}} + 1$

p (x) = x^{3} - 4 x^{2} + x + 6, g (x) = x - 3

(i) p (x) = 2 x^{3} + x^{2} - 2 x - 1, g (x) = x + 1

(i i) p (x) = x^{3} + 3 x^{2} + 3 x + 1, g (x) = x + 2

(i i i) p (x) = x^{3} - 4 x^{2} + x + 6, g (x) = x - 3

x - 2

2 x^{3} - 3 x^{2} - 5 x + 6

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