What are the factors of x^3-10x^2+17x

Question

What are the factors of x^3-10x^2+17x

Answer 1

What are the factors of x³ - 10x² + 17x

• The first one is easy because we can divide each term by x

x(x² - 10x + 17)

• Now we just need to factor the rest of the equation

x² - 10x + 17

• In this case it would be helpful to use the quadratic formula where
• ax² + bx + c = 0
• x = (-b ± √(b² - 4ac)) / 2a

x = (-(-10) ± √((-10)² - 4(1)(17))) / 2(1)

x = (10 ± √(100 - 68)) / 2

x = (10 ± √32) / 2

x = (10 + √32) / 2 and (10 - √32) / 2

• 2 = √4

x = 10/2 + √32 / √4 and 10/2 - √32 / √4

x = 5 + √8 and 5 - √8

x = 5 ± √8

x = 5 ± √(4•2)

x = 5 ± 2√2

• Now we can write our final factored equation

x(x - (5 + 2√2))(x - (5 - 2√2))

 

The factors are x, x - (5 + 2√2), and x - (5 - 2√2)

 

It might also help to look at the math in a better format.

http://www.wyzant.com/resources/files/259784/factoring

Answer 2

x^3-10x^2+17x=

x(x^2-10x+17) =

 

If 0 = x^2-10x+17, then

0 = x^2+2(x)(-5)+(-5)^2-(-5)^2+17

0 = (x-5)^2 - 8

(x-5)^2 = 8 = (2√(2))^2

|x-5| = 2√(2)

x = 5 ± 2√(2)

 

So x(x^2-10x+17) =

x(x-(5 - 2√(2)))(x-(5 + 2√(2)))