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

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$Let p (x) = x^{3} - 3 x^{2} + 4 x + 4 When x - 2 = 0, we have x = 2 Putting x = 2 in p (x), we get : p (2) = {(2)}^{3} - 3 {(2)}^{2} + 4 (2) + 4 = 8 - 12 + 8 + 4 = 8 We have p (2) \neq 0 i . e ., 2 is not the zero of p (x) . ∴ By factor theorem, (x - 2) is not a factor of x^{3} - 3 x^{2} + 4 x + 4 .$

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

Let px=x3-3x2+4x+4When x-2=0, we have x=2Putting x=2 in px, we get: p2=23-322+42+4 =8-12+8+4 =8We have p2≠0i.e., 2 is not the zero of px.∴ By factor theorem, x-2 is not a factor of x3-3x2+4x+4.

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