Question

Check whether 3x+ 10 is a factor of 3xcube +4xsquare− 11x + 30 or not using long division method​

Answer 1

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According to question:-

$3x + 10 = 0$

$3x = - 10$

$x = \frac{ - 10}{3}$

Equation:

${3x}^{3} + {4x}^{2} - 11x + 30 = 0$

$= 3 \times {( \frac{ - 10}{3} })^{3} + 4 \times {( \frac{ - 10}{3} })^{2} - 11 \times ( \frac{ - 10}{3} ) + 30 = 0$

$= (\frac{ - 1000}{9} ) + ( \frac{400}{9} ) + ( \frac{110}{3} ) + (\frac{30}{1} ) = 0$

$= \frac{( - 1000) + 400 + 330 + 270}{9} = 0$

$= \frac{ - 1000 + 1000}{9} = 0$

$= \frac{0}{9} = 0$

$= > 0 = 0$

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