Question

Using factor theorem, factorize the polynomials:

x⁴ + 10x³ + 35x² + 50x + 24

Answer 1

Let f(x) = x⁴ + 10x³ + 35x² + 50x + 24 

Constant term = 24 

Factors of 24 are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

Let x + 1 = 0 or x = -1 

f(-1) = (-1)⁴ + 10(-1)³ + 35(-1)² + 50(-1) + 24

= 1 – 10 + 35 – 50 + 24 

= 0 

f(1) = 0 

(x + 1) is a factor of f(x) 

Likewise, (x + 2),(x + 3),(x + 4) are also the factors of f(x)

Hence f(x) = (x + 1) (x + 2)(x + 3)(x + 4)