Factor 28c+32.
Write your answer as a product with a whole number greater than 1.
The correct answer and explanation is:
To factor the expression 28c+3228c + 32, the first step is to identify the greatest common factor (GCF) of the two terms, 28c and 32.
Step 1: Identify the GCF
The coefficients of the terms are 28 and 32. The factors of 28 are:
- 1, 2, 4, 7, 14, 28.
The factors of 32 are:
- 1, 2, 4, 8, 16, 32.
The largest common factor between 28 and 32 is 4.
Step 2: Factor out the GCF
Now that we know the GCF is 4, we can factor it out from both terms in the expression: 28c+32=4(7c+8).28c + 32 = 4(7c + 8).
Step 3: Check the factorization
To verify that this factorization is correct, we can expand the expression 4(7c+8)4(7c + 8): 4(7c+8)=4×7c+4×8=28c+32.4(7c + 8) = 4 \times 7c + 4 \times 8 = 28c + 32.
Since this matches the original expression, the factorization is correct.
Final Answer:
The factored form of 28c+3228c + 32 is: 4(7c+8).4(7c + 8).
Explanation:
Factoring involves identifying a common factor in all terms of the expression. By factoring out the GCF, we simplify the expression and represent it as a product of a whole number (4) and a binomial (7c + 8). This approach is useful in simplifying expressions and solving equations.