Question

Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (5x+1)(x−8)=0
?(1 point)
Responses

At least one of the factors, (5x+1)
or (x−8)
, must equal 0 for the left side of the equation to equal 0.
At least one of the factors, open paren 5 x plus 1 close paren or open paren x minus 8 close paren, must equal 0 for the left side of the equation to equal 0.

No values of x will make the left side of the equation equal 0.
No values of x will make the left side of the equation equal 0.

Neither of the factors, (5x+1)
or (x−8)
, must equal 0 for the left side of the equation to equal 0.

Answer 1

Based on the Zero Product Property, the statement that must be true about the quadratic equation \((5x+1)(x−8)=0\) is:

**At least one of the factors, (5x+1) or (x−8), must equal 0 for the left side of the equation to equal 0.**

This means that for the product of two factors to equal zero, at least one of the factors must be equal to zero. Therefore, to solve the equation, you would set each factor equal to zero:

1. \(5x + 1 = 0\)
2. \(x - 8 = 0\)

Solving these equations gives the possible values of \(x\).