Question

decide whether it is true or not: x-3 is a factor of 2x^3 - 6x^2 - 5x + 15

Answer 1

hello mate !...


given....


$one \: factor \: is \: \\ x - 3 = 0 \\ \\ x = 3 \\ \\ sub \: this \: value \: in \: eqn.... \\ \\ 2(3) {}^{3} - 6(3) {}^{2} - 5(3) + 15 = 0 \\ \\ 54 - 54 - 15 + 15 = 0 \\ \\ 0 = 0$


➡️ soo given that factor is satisfies the eqn , its true.


hope it helps u

Answer 2

հҽվ!

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$x - 3 = 0 \\ x = + 3 \\ \\ Put\:value\:of \:x\: in\: given \: polynomial \\ \\ 2{x}^{3} - 6{x}^{2} - 5x + 15 = 0 \\ \\ 2{(3)}^{3} - 6{(3)}^{2} - 5(3) + 15 = 0 \\ \\ (2 × 27 ) - 6 ( 9 ) - 15 + 15 = 0 \\ \\ 54 - 54 - 15 + 15 = 0 \\ \\ Yes \: it \: is \:factor \:of \:given\: polynomial$

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