Question

select all correct ways of factoring $-3x - 9$.
$\square$ $-3(x + 3)$
$\square$ $3(x + 3)$
$\square$ $3(-x - 3)$
$\square$ $-3(x - 3)$
$\square$ $3(x - 3)$

Explanation:

Step1: Analyze the first option

Factor out -3 from \(-3x - 9\). Using the distributive property \(a(b + c)=ab+ac\), we have \(-3(x + 3)=-3\times x+(-3)\times3=-3x - 9\). So this option is correct.

Step2: Analyze the second option

Expand \(3(x + 3)=3\times x+3\times3 = 3x+9\), which is not equal to \(-3x - 9\). So this option is incorrect.

Step3: Analyze the third option

Expand \(3(-x - 3)=3\times(-x)+3\times(-3)=-3x - 9\), which matches the original expression. So this option is correct.

Step4: Analyze the fourth option

Expand \(-3(x - 3)=-3\times x-3\times(-3)=-3x + 9\), which is not equal to \(-3x - 9\). So this option is incorrect.

Step5: Analyze the fifth option

Expand \(3(x - 3)=3\times x-3\times3 = 3x-9\), which is not equal to \(-3x - 9\). So this option is incorrect.

Answer:

-3(x + 3), 3(-x - 3)