Questions: Solve each of the following equations using the Principle of Zero Products and match it to its correct pair of solutions on the right. Each pair on the right will be used once. (x+2)(x-3)=0 (x-2)(x+4)=0 (x-4)(x+3)=0 (x-3)(x+4)=0 x=3 or x=-4 x=4 or x=-3 x=3 or x=-2 x=2 or x=-4

Solution Steps

To solve each equation using the Principle of Zero Products, we set each factor equal to zero and solve for \( x \). This will give us the solutions for each equation. We then match these solutions to the given pairs.

For the equation \((x+2)(x-3)=0\), we set each factor to zero:

1. \(x + 2 = 0 \Rightarrow x = -2\)
2. \(x - 3 = 0 \Rightarrow x = 3\)

Thus, the solutions are \(x = -2\) and \(x = 3\).

For the equation \((x-2)(x+4)=0\), we set each factor to zero:

1. \(x - 2 = 0 \Rightarrow x = 2\)
2. \(x + 4 = 0 \Rightarrow x = -4\)

Thus, the solutions are \(x = 2\) and \(x = -4\).

For the equation \((x-4)(x+3)=0\), we set each factor to zero:

1. \(x - 4 = 0 \Rightarrow x = 4\)
2. \(x + 3 = 0 \Rightarrow x = -3\)

Thus, the solutions are \(x = 4\) and \(x = -3\).

For the equation \((x-3)(x+4)=0\), we set each factor to zero:

1. \(x - 3 = 0 \Rightarrow x = 3\)
2. \(x + 4 = 0 \Rightarrow x = -4\)

Thus, the solutions are \(x = 3\) and \(x = -4\).

Now we match the solutions to the provided pairs:

• The solutions \(x = 3\) or \(x = -2\) from the first equation do not match any pairs.
• The solutions \(x = 2\) or \(x = -4\) from the second equation match with \([2, -4]\).
• The solutions \(x = 4\) or \(x = -3\) from the third equation match with \([4, -3]\).
• The solutions \(x = 3\) or \(x = -4\) from the fourth equation match with \([3, -4]\).

Final Answer