Answer:
(x + 1)² (5x + 4)
Step-by-step explanation:
f(x) = 5x³ + 14x² + 13x + 4 ---------->> factor the polynomial completely
use the rational root theorem:
= (x + 1) 5x³ + 14x² + 13x + 4
x + 1
= 5x² + 9x² + 13x + 4
x + 1
= 5x² + 9x² + 4x + 4
x + 1
= 5x² + 9x + 4
break expression into groups
= (5x² + 4x) + (5x + 4)
factor out 5x²+4
= x(5x + 4) (x + 1)
factor out common terms : 5x + 4
= (5x + 4) (x + 1)
= (x+1) (5x + 4) (x + 1)
refine:
= (x + 1)² (5x + 4)
