X^3+3x^2=4 what is The width of x

Question

this models the volume of a shipping container where x is the width. graph the equation 

Answer 1

x³ + 3x² = 4

x³+ 3x² - 4 = 0

 

To factor, we want three factors of -4 that add to +3:  Answer: 2·2·(-1) = -4, 2+2+(-1) = 3.

 

(x+2)(x+2)(x-1) = 0

(x+2)²(x-1) = 0

x = -2 and x = 1

 

Since you can't have a negative length (x=-2), the answer is x = 1.

 

Graph:

• starts at -∞ as x → -∞
• climbs rapidly and touches x-axis at x = -2 then turns down
• crosses y-axis at -4
• turns up and crosses x- axis at x = 1
• climbs rapidly to ∞ as x → ∞