Please help with math?!?!?

Question

find the remainder by division of:

a) x^5 - 4x^4 + x^3 -7x +1 by x+2

b) x^5 - x^4 + x^3 + 2x^2 - x + 4 by x^3+1

the equation 12x^3 - 23x^2 - 3x + 2=0 has a solution x=2. Find all other solution

A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is 3 times its distance from the point B (2, -1). Determine the equation of the curve.

Answer 1

Use synthetic division

a.) x^4 - 6x^3 + 13x^2 - 26x + 45 - 89/(x+2)

Use long division

b.) x^2 - x + 1 + (x^2+3) / (x^3 +1)

Use synthetic division when x = 2 to get the equation

12x^2 + x -1

(3x + 1) (4x - 1)

x = -1/3 and 1/4

Find the locus of points which has a distance equal to 3 times further from (-1, 1) to (2,-1).

Simplify

3√[(x+1)^2 + (y-1)^2] = √[(x-2)^2 + (y+1)^2]

to get

8x^2 + 22x + 8y^2 - 20y = -13

This is an ellipse

Sorry, I could not be more explanatory. The problem is that you posted 4 questions.