The Zero Product Property Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
4 of 54 of 5 Items

Question
Solve the factored quadratic equation (x−5)(x+3)=0
.(1 point)
The smaller solution is x=
, and the larger solution is x=
.
Remaining Attempts : 3

Answer 1

To solve the equation \((x−5)(x+3)=0\), we can use the Zero Product Property, which states that if the product of two factors equals zero, then at least one of the factors must be equal to zero.

Setting each factor equal to zero gives us:

1. \(x - 5 = 0\)
2. \(x + 3 = 0\)

Solving these equations:

1. For \(x - 5 = 0\): \[ x = 5 \]

2. For \(x + 3 = 0\): \[ x = -3 \]

Thus, the solutions are \(x = -3\) and \(x = 5\).

The smaller solution is \(x = -3\), and the larger solution is \(x = 5\).