The quotient of (x4 – 3x2 + 4x – 3) and a polynomial is (x2 + x – 3). what is the polynomial? x4 – 2x2 + 5x – 6 x2 – x + 1 x6 + x5 – 6x4 + x3 + 10x2 – 15x + 9 x4 – 4x2 + 3x

x^2 - x + 1

Step-by-step explanation:

The quotient of (x4 – 3x2 + 4x – 3) and a polynomial is (x2 + x – 3).

To find the polynomial we divide (x^4 – 3x^2 + 4x – 3) divide by (x^2+x-3)

Use long division

                               x^2  - x   + 1

    x^2+x-3             x^4 + 0x^3 -3x^2 +4x-3

                              x^4 + x^3  -3x^2

                          (subtract)

                                      -x^3  +0x^2 + 4x

                                      -x^3  -x^2    +3x    

                            (subtract)

                                              +x^2    +x  -3

                                                x^2   + x  -3

                                 (subtract)

                                               0

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.