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 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. 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.
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 property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. Thus, to solve the equation \((5x+1)(x-8)=0\), you set each factor equal to zero:
1. \(5x + 1 = 0\)
2. \(x - 8 = 0\)
This ensures that the left side of the equation is equal to zero.
**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 property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. Thus, to solve the equation \((5x+1)(x-8)=0\), you set each factor equal to zero:
1. \(5x + 1 = 0\)
2. \(x - 8 = 0\)
This ensures that the left side of the equation is equal to zero.