Final answer:
To factor out the greatest common factor from 18x²-42x, we determine the highest number that divides both coefficients, which is 6, and the lowest power of 'x' in both terms, giving us 6x. Dividing each term by 6x results in the factored expression 6x(3x - 7).
Step-by-step explanation:
The student asked to factor out the greatest common factor from the expression 18x²-42x. To factor out the greatest common factor, we first need to find the highest number that divides both coefficients (18 and 42) and also take out the lowest power of the variable that is present in both terms. The highest number that divides both 18 and 42 is 6, and the lowest power of 'x' present in both terms is 'x'. Thus, the greatest common factor is 6x.
We then divide each term by 6x to factor it out:
- 18x² ÷ 6x = 3x
- 42x ÷ 6x = 7
Now we can write the factored expression as:
6x(3x - 7)