Short Answer 
The answer explains algebraic factors as components that simplify expressions, illustrating this with the factorization of the expression 16x + 80 into 16(x + 5). It also connects algebraic factors to quadratic equations, emphasizing the significance of their roots as real-number solutions.
Step 1: Understanding Algebraic Factors
Algebraic factors are the elements that multiply together to form a given expression. They can be expressed in various forms, including summation and subtraction. When working with algebraic factors, it’s important to recognize that they can simplify complex expressions into more manageable components.
Step 2: Factoring the Expression
To factor the expression 16x + 80, we start by identifying the greatest common factor. In this case, we can take 16 out as a common factor:
- Start with the expression: 16x + 80
- Factor out 16: 16(x + 5)
Thus, the algebraic factor is 16(x + 5).
Step 3: Understanding Roots of Quadratic Equations
Algebraic factors are often linked to quadratic equations, where you may find their roots. The roots of the quadratic equation formed by the factorization are significant features:
- Roots are the solutions to the equation.
- The roots of quadratic equations derived from the factors are typically real numbers.
- For our example, the expression can yield real roots based on the factorization.
This illustrates the relationship between algebraic factors and the characteristics of quadratic equations.