How do you factor ; x^4-7x^3+12x^2+4x-16

Fundemental principle: If a polynomial is 0 when x = k, then (x - k) is a factor!

Trial & error shows that the polynomial = 0 when x = 2

Hence (x - 2) must be a factor

So write as

x^4 - 2 x^3 -5x^3 + 10x^2 + 2x^2 - 4x + 8x - 16

= X^3 (x-2) - 5x^2(x -2) + 2x (x-2) +8 (x - 2)

= (x -2) (X^3 - 5x^2 +2x + 8)

Again X^3 - 5x^2 +2x + 8 = 0 when x = 4, hence it hax (x - 4) as factor!

X^3 - 5x^2 +2x + 8 = x^3 - 4x^2 -x^2 + 4x - 2x + 8
= x^2 (x - 4) - x (x - 4) -2 (x - 4)

= (x^2 -x -2) (x-4)

= (x -2) (x +1) (x -4)

Hence the answer is (x -2) (x - 2) (x +1) (x - 4)

Thanks You, but I'm sorry I still don't understand:confused:

Tell me which part you don't understand

Terry