Question

solve the equation by the zero - factor property.
$x^2 + 8x - 9 = 0$

a. ${0, - 9}$
b. ${3, - 3}$
c. ${- 1,9}$
d. ${1, - 9}$

Explanation:

Step1: Factor the quadratic equation

We need to factor \(x^2 + 8x - 9 = 0\). We look for two numbers that multiply to \(-9\) and add up to \(8\). The numbers are \(9\) and \(-1\) since \(9\times(-1)=-9\) and \(9 + (-1)=8\). So, we can factor the equation as:
\((x + 9)(x - 1)=0\)

Step2: Apply the zero - factor property

The zero - factor property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both).
For \((x + 9)(x - 1)=0\), we set each factor equal to zero:

• Case 1: \(x+9 = 0\)

Subtract \(9\) from both sides of the equation: \(x=-9\)

• Case 2: \(x - 1=0\)

Add \(1\) to both sides of the equation: \(x = 1\)

Answer:

D. \(\{1, - 9\}\)