I've included two questions. hopefully you can me with both.

  1.  value is 0; x-3 is a factor . . . . . . . . . . . . . .third choice

  2.  evaluates at x = -1; remainder is -11 . . . . first choice

Step-by-step explanation:

Dividing f(x) by (x -a) gives ...

  f(x)/(x -a) = g(x) +r/(x -a) . . . . some quotient and a remainder r

If we multiply this expression by (x -a), we see ...

  f(x) = (x -a)g(x) +r

so

  f(a) = (a -a)g(a) +r . . . . . evaluate the above equation at x=a

  f(a) = 0 +r

  f(a) = r . . . . . . . . . a statement of the remainder theorem

If r=0, then x-a is a factor of f(x) = (x-a)g(x).

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1. We have "a" = 3, and f(3) = 0. Therefore (x-3) is a factor.

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2. We have "a" = -1, and f(-1) = -11. Therefore the remainder from division by (x+1) is -11.

they disappear if your absent from to long. i found out that the hard way.

step-by-step explanation:

brainliest lol i just need one more brainliest.

tell you what. i'll find the length of the medians and you can fill in the blanks where they belong.

br

b = (2a,0)

r = (a/2,b/2) remember these things are medians. they go to the 1/2 way point of the line opposite the vertex they face.

br^2 =   (2a - a/2)^2 + (0 - b/2)^2

br^2 = (3/2 a) ^2 + b^2 / 4

br^2 = 9/4 a^2 + b^2 / 4   we need to find some relationship between a and b.

let's try ab = bc  

ab = 2a

bc = (2a - a)^2 + (b - 0)^2

bc = sqrt(a^2 + b^2)

ab = bc

2a = sqrt(a^2 + b^2) square both sides.

4a^2 = a^2 + b^2 subtract a^2 from both sides.

sqrt(3a^2) = sqrt(b^2)

sqrt(3)a = b

let's put b into br^2

br^2 = 9/4 a^2 + 3b^2 / 4

br^2 = 12 a^2 / 4

br^2 = 3a^2 

br = sqrt(3) * a

cp

c = (a,b) ; p = (a,0) this is another application of the distance formula, and it is a good one.

cp^2 = (a - a)^2 + (b - 0)^2

cp^2 = 0 + b^2

cp^2 = b^2 which you can see from the diagram. 

cp = sqrt(b^2)

cp = b but b = sqrt(3) * a 

cp = sqrt(3)*a

aq

a = (0,0)

q = (3/2) a, b/2

aq^2 = (3a/2 -0)^2 + (b/2 - 0)^2

aq^2 = 9a^2/4 + b^2/4

but b = sqrt(3) * a 

aq^2 = 9a^2 / 4 + (sqrt(3)*a)^2 /4

aq^2 = 9 a^2/ 4 + 3 a^2 / 4

aq^2 = 12 a^2/4

aq^2 = 3 a^2

aq = (sqrt  3) * a which agrees with the other two.