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f(x) = ax^3 + bx^2 + cx + d In the polynomial above, a, b, c, and d are constants. If f(–5) = 3, which of the following must be true about f(x)? A x – 3 is a factor of f(x). B The remainder when f(x) is divided by x + 5 is 3. C x + 2 is a factor of f(x). D x + 5 is a factor of f(x).

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Answer:

Step-by-step explanation:

hello

if f(-5)=3 it means that the remainder when f(x) is divided by (x-(-5))=x+5 is 3

so B is correct

The remainder when f(x) is divided by x + 5 is 3.

W have given that,

f(x) = ax^3 + bx^2 + cx + d

In the polynomial above, a, b, c, and d are constants and f(-5)=3.

What is the remainder theorem?

When a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k).

- 5 is the root of the given polynomial when remainder is 3 so we get the one factor of the given polynomial and that is,

x-(-5)=(x+5)

That is if f(-5)=3 it means that the remainder when f(x) is

divided by (x-(-5))=x+5 is 3

Therefore option  B is correct.

To learn more about the remainder theorem visit:

https://brainly.com/question/13328536

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