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.

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

Answers

GPT-4o mini
The statement that must be true based on the Zero Product Property 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 is because the Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. So, in this case, for \((5x + 1)(x - 8) = 0\), either \(5x + 1 = 0\) or \(x - 8 = 0\) must be true for the equation to hold.