Using factor theorem to determine whether (x-2) is a factor of $x^{3} - 3 x^{2} + 4 x + 4$ .

(x - 2)

is a factor

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(x - 2)

is not a factor

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Invalid question

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Cannot be determined

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Solution

The correct option is C $(x - 2)$ is not a factor
Let $p (x) = x^{3} - 3 x^{2} + 4 x + 4$ and
$g (x) = x - 2 = 0$
$\Rightarrow x - 2 = 0$
$\Rightarrow x = 2$
If $g (x)$ is a factor of $p (x)$ , then $p (2)$ should be equal to zero.
$p (2) = x^{3} - 3 x^{2} + 4 x + 4$
$= 2^{3} - 3 (2)^{2} + 4 (2) + 4$
$= 8 - 12 + 8 + 4$
$= 8$
$p (2) \neq 0$
Therefore,
$(x - 2)$ is not a factor of $x^{3} - 3 x^{2} + 4 x + 4$

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Using factor theorem to determine whether (x-2) is a factor of x3−3x2+4x+4.

The correct option is C (x−2) is not a factorLet p(x)=x3−3x2+4x+4 and g(x)=x−2=0 ⇒x−2=0 ⇒x=2If g(x) is a factor of p(x), then p(2) should be equal to zero. p(2)=x3−3x2+4x+4 =23−3(2)2+4(2)+4 =8−12+8+4 =8 p(2)≠0Therefore,(x−2) is not a factor of x3−3x2+4x+4

Using factor theorem to determine whether (x-2) is a factor of $x^{3} - 3 x^{2} + 4 x + 4$ .