Problem 20

Question

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$32 x-24$$

Step-by-Step Solution

Verified
Answer
The greatest common factor of the terms in the polynomial is 8. So, the factored form of the polynomial is \(8(4x - 3)\)
1Step 1: Identify the Greatest Common Factor (GCF)
In the polynomial \(32x - 24\), both terms, 32x and 24, share a common factor of 8.
2Step 2: Express the polynomial as a product of the GCF
To express the polynomial as a product of the GCF, divide each term by the GCF. So, \(32x - 24 = 8(4x - 3)\)
3Step 3: Check your factorization
To confirm the factorization is accurate, distribute the factor back across the brackets: \(8(4x - 3) = 32x - 24 \). As this statement is true, the factorization \(8(4x - 3)\) is correct.