Factor 30p+12q.
Write your answer as a product with a whole number greater than 1.
The correct answer and explanation is:
To factor the expression 30p + 12q, you first need to identify the greatest common factor (GCF) of the two terms.
Step 1: Find the GCF of 30p and 12q.
- The GCF of the numerical coefficients (30 and 12) is 6, because 6 is the largest number that divides both 30 and 12.
- The variables in the terms are p and q. Since there are no common variables between the two terms, the GCF only includes the numerical part, which is 6.
Step 2: Factor out the GCF.
You can now factor out the GCF of 6 from the entire expression: 30p+12q=6(5p+2q)30p + 12q = 6(5p + 2q)
Step 3: Verify the factorization.
To check if the factorization is correct, distribute the 6 back into the terms inside the parentheses: 6(5p+2q)=6×5p+6×2q=30p+12q6(5p + 2q) = 6 \times 5p + 6 \times 2q = 30p + 12q
This confirms that the factorization is correct.
Final Answer:
The factored form of 30p + 12q is 6(5p + 2q).
Explanation:
Factoring an expression like this involves finding the largest number that can divide both the numerical coefficients (in this case, 30 and 12). This process simplifies the expression by pulling out the common factor, making the expression easier to work with. After factoring, the remaining terms inside the parentheses should still represent the original expression when multiplied back. This method is useful for simplifying algebraic expressions and solving equations more efficiently.