x^2 + x - 12
Since 'x^2' term has a coefficient of '1' (N0 number), then we look at the constant, which is '12'.
We need two number that multiply to '12' and 'add' to '1'
The factors of '12' are, 1,12 : 6,2 ; 3,4. This last one satisfies the addition.
Hence
Set up brackets
( x 4 )(x 3)
Which signs? We note that the constant is 'minus' So the signs in the brackets are different. We also note that the 'x' term is positive(+) , so the larger number is positive.
Hence (x 4)(x 3) becomes ( x + 4)( x - 3).
Fully factored!!!!
(x + 5)2
(x - 3)(x - 2)
It can be factored. Whether the factored form is simpler or not is a matter of opinion.sqrt( 16 - x2 ) = sqrt [ (4 + x) (4 - x) ]
x3 - x2 + 2x = x*(x2 - x + 2) which cannot be factored further.
x2+x-6 = (x-2)(x+3) when factored
It is (x+4)(x+5) when factored
(x + 5)2
(x - 3)(x - 2)
It can be factored. Whether the factored form is simpler or not is a matter of opinion.sqrt( 16 - x2 ) = sqrt [ (4 + x) (4 - x) ]
x3 - x2 + 2x = x*(x2 - x + 2) which cannot be factored further.
x2+x-6 = (x-2)(x+3) when factored
x2 + 1 can't be factored in the real numbers. If complex numbers are acceptable, it can be factored as (x + i)(x - i).
6x5(x2 - 6x + 3)
x2 + 5xy - 18y2 can not be factored.
x2 + 5x - 120 can not be factored.
That cannot be factored
It is (x-1)(x-1) when factored