x2 - x - 30 = (x - 6)(x + 5)
The trick is to look for 2 numbers which multiply together to give -30 and sum together to give -1. In this case -6 and 5.
X3 X(X2) X2(X) and, X * X * X
(x+a) (x-a)
Original problem: x^2-x-20x2-25/x2-16x^2-x-30 Revised: [(x2 - x - 20)(x2 - 25)] / [(x2 - 16)(x2 - x - 30)] Solution: Factor the polynomials: {[(x - 5)(x + 4)][(x + 5)(x - 5)]} / {[(x +4)(x - 4)][(x - 6)(x + 5)]} Cancel common factors: [(x - 5)(x - 5)] / [(x - 4)(x - 6)] ---> Simplest form (or final answer) (Optional) Expand: (x2 - 10x + 25) / (x2 - 10x + 24)
x2 - 4x - 32 = (x - 8)(x + 4)
(x-8)(x+8) = x2-64
x2 + 1x - 30 = (x + 6) (x - 5)
(x+5)(x-6)
-28
x^2 - x + 30 doesn't have rational factors. If that was - 30, it would factor to (x - 6)(x + 5)
32
(x + 10)(x - 3)
-28
32
-28
x2 - x + 30 does not have any factors. If on the other hand you wanted to factor out: x2 - x - 30 Then it can be done as follows: = x2 - 6x + 5x - 30 = x(x - 6) + 5(x - 6) = (x + 5)(x - 6)
32
(x - 10)(x - 3)