how do you factor x^3-2x^2+x=-5(x-1)^2?

Question

How do you factor the following step by step?

 

x³-2x²+x=-5(x-1)²

Answer 1

x³ - 2x² + x = -5(x-1)²

 

x(x² - 2x + 1) = -5(x-1)²

 

x(x-1)² + 5(x-1)^{2 = 0}

 

(x-1)²(x+5) = 0

 

x = 1 or x = -5

Answer 2

x³ - 2x² + x = -5(x - 1)²

x(x² - 2x + 1) = -5(x - 1)²

 

When we factor out we have (x + m)(x + n) to define those factors

m + n = b (where b = the center coefficient)

m * n = c (where c is the constant)

-1 - 1 = -2

-1 * -1 = 1

x(x - 1)(x - 1) = -5(x - 1)²

x(x - 1)² = -5(x - 1)²

 

If you're looking for the value of x, we can then divide both sides by (x-1)²:

x = -5

 

Check:

(-5)³ - 2(-5)² + -5 = -5(x - 1)²

-125 - 2*25 - 5 = -5(-6)²

-130 - 50 = -5 * 36

-180 = -180