Question

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 $x = -4$

click and hold an item in one column, then drag it to the matching item in the other column. be sure your cursor is over the target before releasing. the target will highlight or the cursor will change. need help? watch this video.
clear

Explanation:

Step1: Solve \((x + 2)(x - 3)=0\)

By the Zero - Product Principle, if \(ab = 0\), then \(a = 0\) or \(b = 0\). So \(x+2 = 0\) or \(x - 3=0\). Solving \(x + 2=0\) gives \(x=-2\), and solving \(x - 3 = 0\) gives \(x = 3\). So the solutions are \(x = 3\) or \(x=-2\).

Step2: Solve \((x - 2)(x + 4)=0\)

Using the Zero - Product Principle, \(x-2 = 0\) or \(x + 4=0\). Solving \(x-2=0\) gives \(x = 2\), and solving \(x + 4=0\) gives \(x=-4\). So the solutions are \(x = 2\) or \(x=-4\).

Step3: Solve \((x - 4)(x + 3)=0\)

By the Zero - Product Principle, \(x-4 = 0\) or \(x + 3=0\). Solving \(x-4=0\) gives \(x = 4\), and solving \(x + 3=0\) gives \(x=-3\). So the solutions are \(x = 4\) or \(x=-3\).

Step4: Solve \((x - 3)(x + 4)=0\)

Using the Zero - Product Principle, \(x-3 = 0\) or \(x + 4=0\). Solving \(x-3=0\) gives \(x = 3\), and solving \(x + 4=0\) gives \(x=-4\). So the solutions are \(x = 3\) or \(x=-4\).

Answer:

• \((x + 2)(x - 3)=0\) matches with \(x = 3\) or \(x=-2\)
• \((x - 2)(x + 4)=0\) matches with \(x = 2\) or \(x=-4\)
• \((x - 4)(x + 3)=0\) matches with \(x = 4\) or \(x=-3\)
• \((x - 3)(x + 4)=0\) matches with \(x = 3\) or \(x=-4\)