Try to factor
x³ + 4x² + 25
Let add x² then subtract x²
x³ + 5x² - x² + 25
factor x² and -1
x²(x + 5) - 1(x² - 25)
x²(x + 5) -1(x - 5)(x + 5)
Factor x + 5
(x + 5)[x² - (x - 5)]
(x + 5)(x² - x + 5)
If you divide this by (x + 5), the factor (x + 5) cancel out and the answer is x² - x + 5
x³ + 4x² + 25
Let add x² then subtract x²
x³ + 5x² - x² + 25
factor x² and -1
x²(x + 5) - 1(x² - 25)
x²(x + 5) -1(x - 5)(x + 5)
Factor x + 5
(x + 5)[x² - (x - 5)]
(x + 5)(x² - x + 5)
If you divide this by (x + 5), the factor (x + 5) cancel out and the answer is x² - x + 5