Question

Show that 3x+2 is a factor of 3x^2-x-2 using factor theorem

Answer 1

$Let \:p(x) = 3x^{2}-x-2$

$Zero \: of \: 3x + 2 \: is \: x = \frac{-2}{3}$

$p(\frac{-2}{3} ) = 3\Big(\frac{-2}{3}\Big)^{2} - \Big(\frac{-2}{3} - 2 \\= 3 \times \frac{4}{9} + \frac{2}{3} - 2 \\= \frac{4}{3} + \frac{2}{3} - 2 \\= \frac{4+2-6}{3} \\= 0$

$p(\frac{-2}{3} ) = 0$

Therefore.,

$3x+2 \: is \:a \:factor \:of \: 3x^{2}-x-2$

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Answer 2

hope this will help you!