Pls help I need this ASAP with the work pls

9514 1404 393

  (a)  x^4 -3x^3 +x^2 -4

Step-by-step explanation:

Fill in the given expressions and simplify.

  P(x) = R(x) -C(x)

  P(x) = (2x^4 -3x^3 +2x -1) -(x^4 -x^2 +2x +3) . . . . use given R(x), C(x)

  P(x) = 2x^4 -3x^3 +2x -1 -x^4 +x^2 -2x -3 . . . . eliminate parentheses

  P(x) = (2 -1)x^4 +(-3)x^3 +(1)x^2 +(2 -2)x +(-1 -3) . . . . collect terms

  P(x) = x^4 -3x^3 +x^2 -4 . . . . simplify

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!