An algebraic expression that is formed by sums or subtractions of terms can be factored provided there are numeric or variable common factors in all the terms.

The following expression

$Z=12x^4-20x^2+32x$

Can be factored in the constants and in the variable x.

1. To find the common factor of the variable, we must locate if the variable is present in all terms. If so, we take the common factor as the variable with an exponent which is the lowest of all the exponents found throughout the different terms. In this case, the lowest exponent is x (exponent 1).

2. To find the common factors of the constants, we take all the coefficients:

12 - 20 - 32

and find the greatest common divisor of them, i.e. the greatest number all the given numbers can be divided by. This number is 4, since 12/4=3, 20/4=5 and 32/4=8

3. The factored expression is

$Z=12x^4-20x^2+32x=4x(3x^3-5x+8)$

$\boxed{12x^4-20x^2+32x=4x(3x^3-5x+8)}$

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3 years ago