A. Factor the polynomial: x^5-4x^3+8x^2-32
b. Solve by factoring: 2x^2-3x+1=0

a. (x^3+8)(x^2-4)

b. x=1 and x=1/2

Step-by-step explanation:

a. (x^3+8)(x^2-4) = x^5-4x^3+8x^2-32 [foil method: first,outside,inside,last]

b. use quadratic formula: -b +/- square root b^2-4ac / 2a

2=a; -3=b; 1=c

-(-3) + square root (-3)^2 - 4(2)(1) / 2(2)

3 + 1 / 4 = 4/4 = 1

3 - 1/4 = 2/4 = 1/2

step-by-step explanation:

circumference divided by 3.141592654 then timesthe radius twice

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240