Question

show show that x square minus x + 2 is factor of the polynomial 3 x cube minus 4 x square + 7 x - 2
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Answer 1

hope it helped you out

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Answer 2

$Let \: p(x) = 3x^{3}-4x^{2}+7x-2 \:and \\g(x) = x^{2} -x+2$

x²-x+2) 3x³-4x²+7x-2(3x-1

********* 3x³-3x²+6x

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*************** -x²+x-2

*************** -x²+x-2

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Remainder (0)

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$\blue{ (3x^{3}-4x^{2}+7x-2)\:is \:divided\:by }\\\blue {(x^{2} -x+2) \:gives \: 0 \:as \: the \: Remainder}$

$\therefore (x^{2} -x+2) \: is \: a \: factor \:of \\(3x^{3}-4x^{2}+7x-2)$

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