Question

If (3x – 2) is a factor of 3x^3 + x^2

-20x + 12,find other factors​

Answer 1

Answer:

(x-2), (x+3)

Step-by-step explanation:

Three factors of 3x³ + x² -20x + 12

• Divide 3x³ + x² -20x + 12 by (3x-2)
• Result of division comes out to be x² + x - 6
• Factorise the result.....
• (x + 3) (x - 2)

So, the three factors are (3x - 2),(x +3),(x - 2)

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Answer 2

Answer:

(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 a factor of p(x).

3x-2)3x³+x²-20x+12(x²+x-6

***** 3x³-2x²

___________________

******** 3x²-20x

******** 3x²-2x

___________________

*********** -18x+12

*********** -18x+12

______________________

The remainder (0)

______________________

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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