Question

`x^2(x-1)(x-4)-2x^3=-6x^2`

If x > 0, what is one possible solution to the equation above? (Hint: there are two real solutions)

Answer 1

x = 2 and 5

Explanation:

x²(x - 1)(x - 4) - 2x³ = -6x² when x > 0

x²(x - 1)(x - 4) - 2x³ + 6x² = 0

~Use foil to simplify the stuff in parenthesis

x⁴ - 5x³ + 4x² - 2x³ + 6x² = 0

~Combine like terms

x⁴ - 7x³ + 10x² = 0

~Factor

x(x - 2) - 5(x - 2)

~Simplify

(x - 2)(x - 5) = 0

~Solve both factors

x - 2 = 0

x = 2

x - 5 = 0

x = 5

Best of Luck!

Answer 2

• 2 and 5

Explanation:

Solving in steps

• x^2(x - 1)(x - 4) - 2x^3 = -6x^2, x > 0
• x^2(x^2 - 5x + 4) -2x^3 + 6x^2 = 0
• x^4 - 5x^3 + 4x^2 - 2x^3 + 6x^2 = 0
• x^4 - 7 x^3 + 10x^2 = 0
• x^2 - 7x + 10 = 0
• x^2 - 2x - 5x + 10 = 0
• x(x - 2) - 5(x - 2) = 0
• (x - 2)( x - 5) = 0

1. x - 2 = 0 ⇒ x = 2
2. x - 5 = 0 ⇒ x = 5