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Mathematics

Show that 3x + 2 is a factor of 3x2 - x - 2.

Factorisation

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Answer

3x + 2 = 0 ⇒ x = −23-\dfrac{2}{3}

∴ When given polynomial 3x2 - x - 2 is divided by x - 2, the remainder

=3(−23)2−(−23)−2=3×49+23−2=43+23−2=63−2=2−2=0.= 3\Big(-\dfrac{2}{3}\Big)^2 - \Big(-\dfrac{2}{3}\Big) - 2 \\[1em] = 3 \times \dfrac{4}{9} + \dfrac{2}{3} - 2 \\[1em] = \dfrac{4}{3} + \dfrac{2}{3} - 2 \\[1em] = \dfrac{6}{3} - 2 \\[1em] = 2 - 2 = 0.

Hence, by factor theorem 3x + 2 is a factor of 3x2 - x - 2.

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