Use synthetic division method for performing following divisions. Write whether the divisor is a factor of divided. Justify
$(4 x^{4} + 10 x^{3} - 3 x^{2} + 2 x - 21) \div (x + 3)$

It is not a factor of dividend

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It is a factor of dividend

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Cannot be determined

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None of above

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Solution

The correct option is B It is a factor of dividend
$(4 x^{4} + 10 x^{3} - 3 x^{2} + 2 x - 21) \div (x + 3)$
$- 3$ $+ 4 + 10 - 3 + 2 - 21$
$- 12 + 6 - 921$
$+ 4 - 2 + 3 - 70$
Here the reminder is $0$
Hence, $(x + 3)$ is a factor $(4 x^{4} + 10 x^{3} - 3 x^{2} + 2 x - 21)$

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$- 3$	$+ 4 + 10 - 3 + 2 - 21$ $- 12 + 6 - 921$
	$+ 4 - 2 + 3 - 70$