Factor 18u + 14
Write your answer as a product with a whole number greater than 1.
The correct answer and explanation is:
To factor the expression 18u + 14, the first step is to identify the greatest common factor (GCF) of the two terms.
- The two terms are 18u and 14.
- The numerical coefficients are 18 and 14.
- To find the GCF of 18 and 14, list their factors:
- The factors of 18 are: 1, 2, 3, 6, 9, 18.
- The factors of 14 are: 1, 2, 7, 14.
- The largest common factor between 18 and 14 is 2.
Now, factor out the GCF (which is 2) from the expression: 18u+14=2(9u+7)18u + 14 = 2(9u + 7)
Thus, the factored form of 18u + 14 is 2(9u + 7).
Explanation:
- The process of factoring involves identifying the GCF of all terms in the expression.
- Once the GCF is found, it is factored out, and what remains in parentheses is the simplified form of the original expression.
- This method ensures that the expression is written as a product of a whole number greater than 1 (in this case, 2) and a binomial (in this case, 9u+79u + 7).
- This is the simplest and most efficient way to factor the expression, as the GCF is the largest number that divides both 18 and 14 evenly.
Therefore, 2(9u + 7) is the correct factorization of 18u + 14.