Question

divide 6x^3-19x^2+16x-4 by x-2 and use the results to factor the polynomial completely

Answer 1

This is answer of your question

Answer 2

$Let \: p(x) = 6x^{3}-19x^{2}+16x-4 \:and \\g(x) = x-2$

x-2) 6x³-19x²+16x-4(6x²-7x+2

***** 6x³ -12x²

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********** -7x²+16x

********** -7x² + 14x

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****************2x-4

**************** 2x - 4

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Remainder ( 0)

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$Now ,\red{\frac{6x^{3}-19x^{2}+16x-4}{x-2} }\\= (x-2)(6x^{2}-7x+2) \\= (x-2)(6x^{2}-4x-3x+2) \\= (x-2)[2x(3x-2)-1(3x-2)] \\= (x-2)(3x-2)(2x-1)$

Therefore.,

$\red{\frac{6x^{3}-19x^{2}+16x-4}{x-2} }\\\green { = (x-2)(3x-2)(2x-1)}$

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