Question

Show that x-2 is a factor of the polynomial 2x3-6x2 +5x-2.

Answer 1

Answer:

ans. yes x- 2 is the solution of polynomial .

Answer 2

$Let \: p(x) = 2x^{3}-6x^{2}+5x-2$

$and \: g(x) = x -2$

$The \: zero \:of \: g(x) \:is \: 2 .$

$Then \: p(2) = 2\times 2^{3} - 6\times 2^{2} + 5 \times 2 - 2$

$= 2 \times 8 - 6 \times 4 + 10 - 2$

$= 16 - 24 + 8$

$= 24-24$

$= 0$

$So, by \: the \: \green { Factor \: Theorem ,}$

$\green { (x-2) \: is \: a \: factor \: of }$

$\green { 2x^{3}-6x^{2}+5x-2}$

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