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).

Step-by-step explanation:

1. a factor of

2. quotient

3. remainder

4. a factor of

i got this right btw

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

answer: 20

step-by-step explanation:

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3