(-%E2%88%922)(2x%2B10)(x%E2%88%922).jpeg "(2 +10)( −2)(2x+10)(x−2)")
Factoring and Solving the Expression: (2 + 10)( −2)(2x+10)(x−2)
This expression involves multiple factors that we can simplify and solve. Let's break it down step by step:
1. Simplify the Initial Factors
- (2 + 10): This simplifies to 12.
- (−2): This remains as -2.
Now our expression looks like this: 12 * (-2) * (2x + 10) * (x - 2)
2. Simplify Further
- 12 * (-2): This simplifies to -24.
Our expression is now: -24 * (2x + 10) * (x - 2)
3. Factor out Common Factors
- (2x + 10): We can factor out a 2: 2(x + 5)
Our expression is now: -24 * 2(x + 5) * (x - 2)
4. Combine the Constants
- -24 * 2: This simplifies to -48
The fully factored expression is: -48(x + 5)(x - 2)
Finding the Solutions
To find the solutions for this expression, we need to determine the values of x that make the expression equal to zero. Since this is a product of factors, the expression will equal zero when any one of the factors equals zero.
- x + 5 = 0 This gives us x = -5
- x - 2 = 0 This gives us x = 2
Therefore, the solutions for the expression (2 + 10)( −2)(2x+10)(x−2) are x = -5 and x = 2.