In Exercises 49-52, use the Factor Theorem to show that the first polynomial is not a factor of the second polynomial. [Hint: Show that the remainder is not zero.] 49. $x - 2$; $-2x^3 + 4x^2 - 4x + 9$ 50. $x + 3$; $-3x^3 - 9x^2 + 5x + 12$ 51. $x + 2$; $4x^4 + 9x^3 + 3x^2 + x + 4$ 52. $x - 3$; $3x^4 - 8x^3 + 5x^2 + 7x - 3$
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We are given the polynomials $x - 2$ and $-2x^3 + 4x^2 - 4x + 9$. According to the Factor Theorem, if $x - 2$ is a factor of $-2x^3 + 4x^2 - 4x + 9$, then substituting $x = 2$ into the second polynomial should result in 0. Show more…
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