If one factor of the polynomial $x^{3} + 4 x^{2} - 3 x - 18$ is $x + 3,$ then the other factor is

x^{2} + x

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x^{2} + x + 6

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x^{2} + x - 6

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x^{2} - x + 6

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Solution

The correct option is C $x^{2} + x - 6$
$(x + 3) x^{2} + x - 6 \sqrt{x^{3} + 4 x^{2} - 3 x - 18}$
$_x^{3} +_{3 x}^{2} - ----------------- -$
$x^{2} - 3 x - 18$
$_x^{2} + 3 x - --------------- -$
$- 6 x - 18$
$- 6 x - 18$
$+ + - ------------- -$
$0 - ----- -$
Other factor $\to x^{2} + x - 6$

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x^{2} - x - 6

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f (x) = x^{2} + x - 6

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a

For what value of k is the polynomial 2x²+3x³+2xk²+3x+6 exactly divisible by (x+2). Show that (x+3) is a factor of x³+x²-4x+6

- x^{2} + x \sqrt{3} + 6

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