Sure! Let's match each polynomial equation with its correct factorized version and solution step by step:
1. First, we need to match the equation [tex]\(24x - 6x^2 = 0\)[/tex] with its factorized version and solution:
- The factorized version is [tex]\(6x(4 - x) = 0\)[/tex].
- The solutions are [tex]\(x = 0\)[/tex] and [tex]\(x = 4\)[/tex].
2. Next, we match the equation [tex]\(4x - x^2 = 0\)[/tex] with its factorized version and solution:
- The factorized version is [tex]\(x(4 - x) = 0\)[/tex].
- The solutions are [tex]\(x = 0\)[/tex] and [tex]\(x = 4\)[/tex].
3. Then, we match the equation [tex]\(2x^2 + 6x = 0\)[/tex] with its factorized version and solution:
- The factorized version is [tex]\(2x(x + 3) = 0\)[/tex].
- The solutions are [tex]\(x = 0\)[/tex] and [tex]\(x = -3\)[/tex].
4. Finally, we match the equation [tex]\(14x - 7x^2 = 0\)[/tex] with its factorized version and solution:
- The factorized version is [tex]\(7x(2 - x) = 0\)[/tex].
- The solutions are [tex]\(x = 0\)[/tex] and [tex]\(x = 2\)[/tex].
The final matches with detailed steps are as follows:
1. [tex]\(24x - 6x^2 = 0\)[/tex]
- Factorized version: [tex]\(6x(4 - x) = 0\)[/tex]
- Solution: [tex]\(x = 0, x = 4\)[/tex]
2. [tex]\(4x - x^2 = 0\)[/tex]
- Factorized version: [tex]\(x(4 - x) = 0\)[/tex]
- Solution: [tex]\(x = 0, x = 4\)[/tex]
3. [tex]\(2x^2 + 6x = 0\)[/tex]
- Factorized version: [tex]\(2x(x + 3) = 0\)[/tex]
- Solution: [tex]\(x = 0, x = -3\)[/tex]
4. [tex]\(14x - 7x^2 = 0\)[/tex]
- Factorized version: [tex]\(7x(2 - x) = 0\)[/tex]
- Solution: [tex]\(x = 0, x = 2\)[/tex]
