Final answer:
To factor the expression -6x^2 + 18x, we extract the greatest common factor, which is -6x, resulting in the factored form -6x(x - 3).
Step-by-step explanation:
The student has asked to factor the expression -6x^2 + 18x. This involves finding common terms or factors and expressing the original expression as a product of simpler expressions. In this case, we can factor out a -6x which is common to both terms.
Here is the step-by-step factorization:
- Identify the greatest common factor (GCF) for both terms. The GCF here is -6x.
- Write the original expression divided by the GCF. So we get -6x(x - 3).
- Check by expanding the factored expression, which should give us the original expression back. And indeed, (-6x)*x + (-6x)*(-3) = -6x^2 + 18x.
Therefore, the factored form of the expression is -6x(x - 3).