What is the completely factored form of f (x) = x^3 - 7x^2 + 2x + 4

f (x) = (x-1) (x²-6x-4)

Step-by-step explanation:

f (x) = x³-7x²+2x+4

using trial

and error

method

f (1) = 1³-7 (1) ²+2 (1) + 4

= 7-7

= 0

∴ (x - 1) is a factor of f (x)

f (x) = (x-1) (x² + bx - 4)

= x³+bx²-4x-x²-bx+4

= x³ + (b-1) x² + (-4-b) x+4

comparing the

coefficients

x² = > b-1 = - 7

b = - 6

x = > - 4-b = 2

-b = 6

b = - 6

∴f (x) = (x-1) (x²-6x-4)