Based on the zero product property which of the following statements must be true about the quadratic equation: (5x + 1)(x-8)=0

Question

A. No values of x will make the left side of the equation equal 0
B. At least one of the factors, (5x + 1) or (x-8) must equal 0 for the left side of the equation to equal 0
C. Neither of the factors (5x + 1) or (x-8) must equal 0 for the left side of the equation to equal 0

Answer 1

The correct answer based on the zero product property is:

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

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, for the equation \((5x + 1)(x-8) = 0\) to hold true, at least one of the factors must equal zero.