determine whether (3x-2)is the factor of 3xcube +x square -20x +12
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no it is not a factor of following polynomial
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P(x) = 3x^3 +x^2 - 20x +12
g(x) = 3x-2
=> 3x - 2 = 0
=> x = 2/3
By Remainder theoram,
P(2/3) = 3(2/3)^3 +(2/3)^2 - 20(2/3) +12
= 8/9 + 4/9 - 40 / 3 + 12
= ( 8 + 4 - 120 + 108) / 9
= (12+108 - 120)/9
= (120-120)/9
= 0/9
= 0
P(2/3) = 0
Remainder = 0
So, g(x) is a factor of P(x)
g(x) = 3x-2
=> 3x - 2 = 0
=> x = 2/3
By Remainder theoram,
P(2/3) = 3(2/3)^3 +(2/3)^2 - 20(2/3) +12
= 8/9 + 4/9 - 40 / 3 + 12
= ( 8 + 4 - 120 + 108) / 9
= (12+108 - 120)/9
= (120-120)/9
= 0/9
= 0
P(2/3) = 0
Remainder = 0
So, g(x) is a factor of P(x)
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