(x-6).jpeg "(x-2)(x-6)")
Factoring and Solving the Expression (x-2)(x-6)
The expression (x-2)(x-6) represents a product of two binomials. Let's explore its factorization, solving for its roots, and understanding its meaning.
Factoring
The expression is already factored. We have two binomials: (x-2) and (x-6).
Solving for Roots
To find the roots of the expression, we need to solve the equation:
(x-2)(x-6) = 0
This equation is true when either of the factors equals zero. So, we have two possible solutions:
- x - 2 = 0 => x = 2
- x - 6 = 0 => x = 6
Therefore, the roots of the expression (x-2)(x-6) are x = 2 and x = 6.
Graphing the Expression
The expression (x-2)(x-6) represents a parabola. The roots we found, x = 2 and x = 6, are the points where the parabola intersects the x-axis. The parabola opens upwards because the coefficient of the x² term (which is 1) is positive.
Understanding the Expression
This expression is a simple quadratic equation. Understanding its factorization and roots is fundamental for solving various mathematical problems in algebra and calculus. It helps us understand how to find the zeros of a function and how to interpret the behavior of quadratic equations.