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.
?(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.
Answers
GPT-4o mini
Based on the Zero Product Property, the correct statement 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, at least one of the factors must be zero. Therefore, in the equation \((5x+1)(x−8)=0\), either \(5x+1=0\) or \(x−8=0\) must be true for the equation to hold.
**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, at least one of the factors must be zero. Therefore, in the equation \((5x+1)(x−8)=0\), either \(5x+1=0\) or \(x−8=0\) must be true for the equation to hold.