SOLUTION: The polynomial (x - 2) is a factor of the polynomial F(x) = 3x^2

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Question 144991: The polynomial (x - 2) is a factor of the polynomial F(x) = 3x^2 - 8x + 2.
True or false
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
First let's factor

Looking at we 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 cannot be factored

So (x - 2) is NOT a factor of

So the statement is false

SOLUTION: The polynomial (x - 2) is a factor of the polynomial F(x) = 3x^2 - 8x + 2. True or false