Question

Factor the expression 5x^3 - x^2 + 5x - 1

Answer 1

Hello,

5x^3-x^3+5x-1=x²(5x-1)+(5x-1)=(5x-1)(x²+1)=(5x-1)(x-i)(x+i)

Answer 2

$5 x^{3} - x^{2} + 5x - 1$

Group like terms
$( 5x^{2} - x^{2} ) + (5x - 1)$

Find the common factor of each term and simplify
$x^{2} (5x - 1) + 1 (5x - 1)$
$( x^{2} + 1) (5x - 1)$




Additional :-
Find the roots of each of the terms:
(i) $( x^{2} + 1)$
      - using the quadratic equation ($x = \frac{-b (+ or -) \sqrt{ b^{2} - 4ac } }{2a}$)
      -  $\frac{-0 + \sqrt{0^{2 - 4(1)(1)} } }{2}$     OR     $\frac{-0 - \sqrt{0^{2 - 4(1)(1)} } }{2}$ 
      - Since the discriminant is negative ($\sqrt{-4}$) [a negative number cannot be rooted] then this equation has no real roots (imaginary roots)

(ii) $5x - 1$
         - Simply Solve for x
              5x - 1 = 0
                    5x = 1
                      x = $\frac{1}{5}$

Thus the only solution this has or the only root this expression has is $\frac{1}{5}$   OR  0.2