B. If (3x-2) is a factor of 3x?+x²-20x+12, find other factors.
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(x-2) and (x+3) are other two factors
Let p(x)=3x³+x²-20x+12,
g(x)=3x-2
It is given that g(x) is factor of p(x).
3x-2)3x³+x²-20x+12(x²+x-6
3x³-2x²
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3x²-20x
3x²-2x
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-18x+12
-18x+12
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Remainder (0)
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BY DIVISION
p(x)=g(x)(x²+x-6)
= (3x-2)(x²+3x-2x-6)
= (3x-2)[x(x+3)-2(x+3)]
= (3x-2)(x+3)(x-2)
Therefore,
(x-2) and (x+3) are other two factors of p(x)
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