Determine whether (3x — 2) is a factor of 3x³ + x² - 20x + 12?

Let p(x) = 3x³ + x² - 20x + 12
We see that

$straight P open parentheses 2 over 3 close parentheses equals 3 open parentheses 2 over 3 close parentheses cubed plus open parentheses 2 over 3 close parentheses squared minus 20 open parentheses 2 over 3 close parentheses plus 12 space space space space space space space space left enclose space space space 3 straight x minus 2 end enclose space equals space 0 space space space space space rightwards double arrow space straight x space 2 over 3 space space space space space space equals 8 over 9 plus 4 over 9 minus 40 over 3 plus 12 space space space space space space equals space 0$

Hence by converse of factor theorem, (3x - 2) is a factor of p(x).

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Determine whether (3x — 2) is a factor of 3x3 + x2 - 20x + 12?

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Determine whether (3x — 2) is a factor of 3x³ + x² - 20x + 12?