3x-12x ^ 2 factorization common factor （1）3x-12x^2 （2）x(x-y)+y(y-x)

3x-12x ^ 2 factorization common factor （1）3x-12x^2 （2）x(x-y)+y(y-x)

3x-12x^2=3x(1-4x)
（2）x(x-y)+y(y-x)=(x-y)^2

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

Do you mean to factorize this equation? Your last term should be n + 1, which is the exponent of X?
3x^n(1-x)-2(x^n-2x^(n+1) )
=3x^n-3x^(n+1)-2x^n+4x^(n+1))
=x^n+x^(n+1)
=x^n(1+x)

How to extract the common factor? X ^ 3 + 3x ^ 2 + 4

No one answers because it can't be decomposed. In a rational field, it's a prime polynomial
Q := RationalField();
> P := PolynomialRing(Q);
F:= X^3+3*X^2+4 ;F;
Factorization(F);
X^3 + 3*X^2 + 4
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