To factorise (x^2 - 1), you can recognize it as a difference of squares, which follows the formula (a^2 - b^2 = (a - b)(a + b)). Here, (a = x) and (b = 1). Thus, (x^2 - 1) can be factored as ((x - 1)(x + 1)).
x2 + 6x = x*(x + 6)
38
1
x4 - x3 - x - 1 rewriting: = x4 - 1 - x3 - x factorising pair of terms: =(x2 + 1)*(x2 - 1) - x*(x2 + 1) = (x2 + 1)*(x2 - 1 - x) or (x2 + 1)*(x2 - x - 1) which cannot be factorised further.
4(x2 + 4)
1(x2-1)
X2 + 4xx(x + 4)=======
x2 + 6x = x*(x + 6)
x2-196 = (x-14)(x+14) when factored
38
1
x4 - x3 - x - 1 rewriting: = x4 - 1 - x3 - x factorising pair of terms: =(x2 + 1)*(x2 - 1) - x*(x2 + 1) = (x2 + 1)*(x2 - 1 - x) or (x2 + 1)*(x2 - x - 1) which cannot be factorised further.
1
x(x+5)
4(x2 + 4)
( x - 14 ) ( x + 14 )
(x2 + 1) = (x2 - i2) with the factors (x+i)(x-i) where i is the square root of (-1).If you don't allow complex numbers (which is usually the case in school mathematics) then there is no factorisation.