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Use the remainder theorem to complete the informal proof for the following statement. If x = -5 is a root of f(x), then (x + 5) must be f(x). Find the of f(x) and (x + 5). The of this operation is 0. Thus, (x + 5) is f(x). Therefore, x = -5 is a root of f(x).

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Answer:


Step-by-step explanation:

1. a factor of

2. quotient

3. remainder

4. a factor of

i got this right btw

Answer:

1. If x = -5 is a root of f(x), then (x + 5) must be a Factor of f(x).

2. Find the Quotient of f(x) when f(x) is divided  by  (x + 5).

3. Then Remainder of this operation is 0.

4. Thus, (x + 5) is Factor f(x).

5. Therefore, x = -5 is a root of f(x).

Remainder Theorem States that

→→Divisor = Dividend × Quotient + Remainder

→ f(x)= (x+5)×Quotient +0

→f(x)=Quotient× (x+5)

Quotient

         [tex]=\frac{f(x)}{x+5}[/tex]

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