Expression Factorization B7Efa1

1. **State the problem:** Simplify or analyze the expression $$828x + 1440$$. 2. **Identify the terms:** The expression consists of two terms: $$828x$$ (a term with variable $$x$$) and $$1440$$ (a constant term). 3. **Check for common factors:** To simplify, find the greatest common divisor (GCD) of $$828$$ and $$1440$$. 4. **Calculate GCD:** - Prime factors of $$828$$: $$2 \times 2 \times 3 \times 3 \times 23$$ - Prime factors of $$1440$$: $$2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5$$ - Common factors: $$2 \times 2 \times 3 = 12$$ 5. **Factor out the GCD:** $$828x + 1440 = 12(69x + 120)$$ 6. **Result:** The expression factored by the greatest common factor is $$12(69x + 120)$$. This is the simplest factorization using integer factors.