Question

a student was asked to solve $4x^2 - 12x = 0$ by factoring out the gcf. at what step did the student first make an error? given: $4x^2 - 12x = 0$ step 1: $4x(x + 3) = 0$ step 2: $4x = 0$ and $x + 3 = 0$ step 3: $x = 0$ and $x = -3$ (1 point) step 1 step 2 step 3

Explanation:

Step 1: Analyze the original equation

The given equation is \(4x^2 - 12x = 0\). To factor out the GCF (Greatest Common Factor), we look for the largest factor common to both terms. The GCF of \(4x^2\) and \(-12x\) is \(4x\).

Step 2: Check Step 1

In Step 1, the student wrote \(4x(x + 3)=0\). But when we factor out \(4x\) from \(4x^2 - 12x\), we should get \(4x(x - 3)=0\) (because \(\frac{-12x}{4x}=- 3\), not \(+3\)). So Step 1 has an error in the factoring.

Step 3: Verify other steps (optional but for clarity)

If we assume Step 1 was correct (even though it's not), Step 2 would be solving \(4x = 0\) and \(x + 3 = 0\), and Step 3 would be finding \(x = 0\) and \(x=-3\). But the error starts at Step 1.

Answer:

Step 1