Q. \[ x^2 – 4x \]
Answer
To factor \(x^2-4x\), factor out the greatest common factor \(x\):
\[
x^2 – 4x = x(x – 4)
\]
Final result: \(x(x-4)\).
Detailed Explanation
We are given the expression \(x^2 – 4x\). Step 1 is to factor it, if possible.
Step 1: Identify the common factor
Look at both terms:
\(x^2\) and \(-4x\).
Both terms contain the factor \(x\). So we can factor out \(x\).
Step 2: Factor out \(x\)
Write the expression as \(x\) times what remains:
\[
x^2 – 4x = x(x – 4).
\]
Final Answer
The factored form of \(x^2 – 4x\) is \(x(x – 4)\).
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Algebra FAQ
Factor \(x^2-4x\).
\[x^2-4x=x(x-4).\]
Find the zeros of \(x^2-4x\).
\[x^2-4x=0 \Rightarrow x(x-4)=0 \Rightarrow x=0 \text{ or } x=4.\]
Expand \(x(x-4)\) to check.
\[x(x-4)=x^2-4x.\]
Solve \(x^2-4x=0\).
\[x^2-4x=0 \Rightarrow x(x-4)=0 \Rightarrow x=0 \text{ or } x=4.\]
What is the GCF of \(x^2-4x\)?
The greatest common factor is \(x\), so \[x^2-4x=x(x-4).\]
Write \(x^2-4x\) in vertex form.
Complete the square: \[x^2-4x=(x-2)^2-4.\]
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