First, let's factor 3x²-8x+2
Looking at wee can see that the first term is and the last term is <span> 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 </span>
<span>
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 </span>
<span> <span><span> <span> First Number Second Number Sum</span> </span> <span> <span> 1 6 1+6=7</span> </span> <span> <span> 2 3 2+3=5</span> </span> <span> <span> -1 -6 -1+(-6)=-7</span> </span> <span> <span> -2 -3 -2+(-3)=-5</span> </span> </span></span>
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<span>
So the statement is false</span>
