Question 144991
First let's factor {{{3x^2-8x+2}}}






Looking at {{{3x^2-8x+2}}} we can see that the first term is {{{3x^2}}} and the last term is {{{2}}} 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


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">6</td><td>1+6=7</td></tr><tr><td align="center">2</td><td align="center">3</td><td>2+3=5</td></tr><tr><td align="center">-1</td><td align="center">-6</td><td>-1+(-6)=-7</td></tr><tr><td align="center">-2</td><td align="center">-3</td><td>-2+(-3)=-5</td></tr></table>

None of these pairs of factors add to -8. So the expression {{{3x^2-8x+2}}} cannot be factored





So (x - 2) is NOT a factor of {{{3x^2-8x+2}}}



So the statement is false