Perform the operation indicated, then place the answer in the proper location on the grid. write your answer in descending powers of x. what must be added to 3x -7 to make x 2 + 4x -1?

x² + x + 6

Step-by-step explanation:

We have to find the expression that must be added to (3x - 7) to make it (x² + 4x - 1).

To get the expression we have to subtract (3x - 7) from (x² + 4x - 1).

Now, (x² + 4x - 1) - (3x - 7)

= x² + x + 6

Therefore, (x² + x + 6) must be added to (3x - 7) to get the result (x² + 4x - 1).

So, the answer is x² + x + 6, which is in the descending power of x. (Answer)

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!