Question

determine whether 3 x minus 2 is a factor of 3 x cube + x square - 20 X + 12​

Answer 1

Answer:

( 3x-2) is a factor of 3x^3+x^2-20 x +12

Step-by-step explanation:

(x-2) and (x+3) are other two factors

Step-by-step explanation:

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 algorithm:

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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