Question

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).

Answer 1

Explanation:

1. a factor of

2. quotient

3. remainder

4. a factor of

i got this right btw

Answer 2

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

`=(f(x))/(x+5)`