\(5 x^{3} - x^{2} + 5x - 1\)
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
