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

According To Synthetic Division Below Which Of The Following Statements Are True class=

Sagot :

xKelvin

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.

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