Question

Select the correct answer from each drop-down menu.

Consider the expression below.
(+4)= + 9)
For (x + 4)(x + 9) to equal O, either (x + 4) or (x + 9) must equal { }
The values of x that would result in the given expression being equal to 0, in order from least to greatest, are { }
and { }

Answer 1

`\textsf{For $(x + 4)(x + 9)$ to equal $0$, either $(x + 4)$ or $(x + 9)$ must equal $\boxed{0}$}\:.`

`\textsf{The values of $x$ that would result in the given expression being equal to $0$,}`

`\textsf{in order from least to greatest, are $\boxed{-9}$ and $\boxed{-4}$}\:.`

Explanation:

`\boxed{\begin{minipage}{8.4cm}\underline{Zero Product Property}\\\\If $a \cdot b = 0$ then either $a = 0$ or $b = 0$ (or both).\\\end{minipage}}`

According to the Zero Product Property, for (x + 4)(x + 9) to equal zero, then either (x + 4) or (x + 9) must equal zero.

Set each factor equal to zero and solve for x:

`\begin{aligned} (x+4)&=0\\x+4&=0\\x+4-4&=0-4\\x&=-4\end{aligned}`
`\begin{aligned} (x+9)&=0\\x+9&=0\\x+9-9&=0-9\\x&=-9\end{aligned}`

Therefore, the values of x that would result in the given expression being equal to zero, in order from least to greatest, are -9 and -4.