Using factor theorem, factorise x⁴-x³-7x²+x+6

(x-1) (x-3) (x+1) (x+2)

Step-by-step explanation:

x⁴-x³-7x²+x+6=

x⁴-x³-x²+x - 6x²+6=

x³ (x-1) - x (x-1) - 6 (x²-1) =

x³ (x-1) - x (x-1) - 6 (x-1) (x+1) =

(x-1) (x³-x-6x-6) =

(x-1) (x³-3x²+3x²-9x+2x-6) =

(x-1) (x-3) (x²+3x+2) =

(x-1) (x-3) (x²+x+2x+2) =

(x-1) (x-3) (x+1) (x+2)

Add and subtract the second term to the expression and factor by grouping.

(x-1) (x+1) (x-3) (x+2)