# x cubed - x squared + 8x - Factor Polynomial

by Zachary
(CA, USA)

How do i factor the polynomial

P(x) = x³ - x² + 8x

for this problem, begin by finding the common factor in all three terms

factor out this common factor

the result will be a polynomial which is much easier to work with

### Comments for x cubed - x squared + 8x - Factor Polynomial

 May 21, 2012 Factor x³ - x² + 8x by: Staff Question: by Zachary (CA, USA) How do i factor a polynomial? Answer: P(x) = x³ - x² + 8x P(x) = x*(x² - x + 8) This equation cannot be factored beyond this point, unless you are willing to use complex numbers. >>> the final answer is: P(x) = x*(x² - x + 8) However, “if” you are willing to use complex numbers (where i = √(-1) , you can calculate the other two roots using the quadratic formula: ax² + bx + c = 0 x = [-b ± √(b² - 4ac)]/(2a) x² - x + 8 = 0 x = unknown a = +1 b = -1 c = +8 x = {-(-1) ± √[(-1)² - 4*1*(8)]}/(2*1) x = {1 ± √(1 - 32)}/2 x = {1 ± √(-31)}/2 x = 1/2 ± √(-31)/2 x = 1/2 ± i√(31)/2 x = 0.5 ± 0.5i√(31) x₁ = 0.5 + 0.5i√(31) x₁ ≈ 0.5 + 0.5*i*5.56776436283 x₁ ≈ 0.5 + 2.783882181415*i x₂ = 0.5 - 0.5i√(31) x₂ ≈ 0.5 - 0.5*i*5.56776436283 x₂ ≈ 0.5 - 2.783882181415*i When complex numbers (where i = √(-1) are used, the final answer is: P(x) = x*[x - 0.5 + 0.5i√(31)]*[x - 0.5 - 0.5i√(31)] or P(x) = x * (x - 0.5 + 2.783882181415*i) * (x - 0.5 - 2.783882181415*i) ---------------------------------------------------------------------------------- Check the answer by multiplying the three factors together: P(x) = x*[x - 0.5 + 0.5i√(31)]*[x - 0.5 - 0.5i√(31)] P(x) = x*{[x - 0.5 + 0.5i√(31)]*[x - 0.5 - 0.5i√(31)]} P(x) = x*{x² - 2*x*(0.5) + (0.5)² - [0.5i√(31)]²} P(x) = x*{x² - x + 0.25 – (0.5)²*i²*[√(31)]²} P(x) = x*{x² - x + 0.25 – (0.25)*i²*(31)} P(x) = x*{x² - x + 0.25 – (7.75)*i²} P(x) = x*{x² - x + 0.25 – (7.75)*[√(-1)]²} P(x) = x*{x² - x + 0.25 – (7.75)*(-1)} P(x) = x*{x² - x + 0.25 + 7.75} P(x) = x*{x² - x + 8} P(x) = x³ - x² + 8x, OK → the three factors are valid Thanks for writing. Staff www.solving-math-problems.com