Question

According to Synthetic division below, which of the following statements are true

Answer 1

B, E, and F.

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:

`3x^2-11x+10`

Our divisor will be (x - a), where a is the number on the very top left.

So, a = 2.

Thus, our divisor is:

`(x-2)`

Note that our remainder is 0.

So, the synthetic division shown is telling us that:

`( 3x^2 - 11x + 10) / (x-2) = 3x - 5`

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.