Question

determine whether (3x-2) is a factor x^3 -6x^2+7x-12

Answer 1

Answer:

No, its not a factor.

Step-by-step explanation:

Here f(x) = x³ - 6x² + 7x - 12.

g(x) = 3x - 2.

3x - 2 = 0.

3x = 2.

x = 2/3.

Now put this value in p(x).

p(2/3) = (2/3)³ - 6(2/3)² + 7(2/3) - 12.

= 8/27 - 24/9 + 14/3 - 12.

= 8/27 - 8/3 + 14/3 - 12.

= 8/27 + 6/3 - 12.

= 8/27 + 2 - 12.

= 8/27 - 10.

= 8 - 270/27

= -262/10.

Since the remainder is NOT ZERO,

Therefore 3x - 2 is not a factor.

Hope it helps.

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