Look at the work shown for the division problem shown on the right. The remainder is
.
Divide 2x4- 4x3 - 11x2 + 3x - 6 by x + 2.

A vertical line and horizontal line combine to make a L shape. There are two rows of entries in the shape. The first row includes 2, negative 4, negative 11, 3, negative 6. The second row includes blank, negative 4, 16, negative 10, 14. On the outside of the shape to the left of the first row is entry negative 2. On the outside of the shape below is a third row of entries that includes 2, negative 8, 5, negative 7, 8.

8

Step-by-step explanation:

Fill in the blank

the answer is a

step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12