Factor 2r + 18 .
Write your answer as a product
The correct answer and explanation is:
To factor the expression 2r+182r + 18, follow these steps:
- Identify the greatest common factor (GCF):
The terms in the expression are 2r2r and 1818. Both terms share a factor of 2. The greatest common factor is 2. - Factor out the GCF:
To factor the expression, divide both terms by the GCF, which is 2: 2r+18=2(r+9)2r + 18 = 2(r + 9)
So, the factored form of the expression is 2(r+9)2(r + 9).
Explanation:
- Step 1: In any expression, factoring means finding the largest factor common to all terms. In 2r+182r + 18, both terms, 2r2r and 1818, share a factor of 2. The greatest common factor, or GCF, of 2 and 18 is 2.
- Step 2: After identifying the GCF, we divide each term of the expression by the GCF. Dividing 2r2r by 2 gives rr, and dividing 1818 by 2 gives 9.
- Step 3: After factoring out 2, you are left with the expression inside the parentheses, (r+9)(r + 9). This represents the two terms that were left after dividing each term of the original expression by the GCF.
Thus, the expression is now factored as 2(r+9)2(r + 9), which is the product of 2 and the binomial (r+9)(r + 9). This is the simplest form of the factored expression.