Answer:
B, E, and F.
Step-by-step explanation:
We can apply synthetic division when dividing a polynomial P(x) by a binomial in the form (x - a).
Looking at the coefficients, we can see that our dividend is:
[tex]3x^2-11x+10[/tex]
Our divisor will be (x - a), where a is the number on the very top left.
So, a = 2.
Thus, our divisor is:
[tex](x-2)[/tex]
Note that our remainder is 0.
So, the synthetic division shown is telling us that:
[tex]( 3x^2 - 11x + 10) \div (x-2) = 3x - 5[/tex]
Hence, E is the correct choice. A uses the incorrect divisor.
If the divisor successfully divides with no remainder, then the divisor is a factor.
Since (x - 2) successfully divided with no remainder, (x - 2) is indeed a factor of the polynomial.
Hence, B is also correct.
C uses the wrong factor.
D uses the wrong value. It should be positive 2.
So, F is the correct choice.
Therefore, the answers are: B, E, and F.
