Factor 6p + 9q.
Write your answer as a product with a whole number greater than 1.
The correct answer and explanation is:
The expression 6p+9q6p + 9q can be factored by finding the greatest common factor (GCF) of the two terms. To do this, we first identify the factors of each term:
- The factors of 6 are 1, 2, 3, and 6.
- The factors of 9 are 1, 3, and 9.
The greatest common factor of 6 and 9 is 3, because 3 is the largest number that divides both 6 and 9 evenly.
Next, we factor out the GCF (3) from the expression: 6p+9q=3(2p+3q)6p + 9q = 3(2p + 3q)
Now, the expression is written as a product of 3 and 2p+3q2p + 3q. This is the fully factored form of the original expression.
In the factored form 3(2p+3q)3(2p + 3q), 3 is the common factor that we factored out from both terms. The expression 2p+3q2p + 3q cannot be factored further because the terms inside the parentheses do not share any common factors.
To verify the factorization, we can distribute the 3 back into the parentheses: 3(2p+3q)=3×2p+3×3q=6p+9q3(2p + 3q) = 3 \times 2p + 3 \times 3q = 6p + 9q
This confirms that the factorization is correct. Therefore, the factored form of 6p+9q6p + 9q is: 3(2p+3q)3(2p + 3q)