The polynomial (x - 2) is a factor of the polynomial 3x2 - 8x + 2.

First, let's factor 3x²-8x+2

Looking at wee can see that the first term is and the last term is where the coefficients are 3 and 2 respectively.

Now multiply the first coefficient 3 and the last coefficient 2 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient - 8? Let's list all of the factors of 6:

Factors of 6:

1,2,3,6

-1,-2,-3,-6 ... List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 6

1*6

2*3

(-1) * (-6)

(-2) * (-3)

note: remember two negative numbers multiplied together make a positive number

Now, which of these pairs add to - 8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to - 8

First Number Second Number Sum 1 6 1+6=7 2 3 2+3=5 - 1 - 6 - 1 + (-6) = - 7 - 2 - 3 - 2 + (-3) = - 5

None of these pairs of factors add to - 8.

So the expression 3x²-8x+2 cannot be factored.

So (x - 2) is NOT a factor of 3x²-8x+2

So the statement is false