Q. \(x^2 + 16x\)

Q: What is the greatest common factor (GCF) of x^2+16x?

The GCF is x, so the expression becomes x(x+16).

Q: Solve x^2+16x=0 by completing the square.

x^2+16x=(x+8)^2-64. Set to zero: (x+8)^2=64 so x=-8\pm 8, giving x=0,-16.

Q: What are the vertex and axis of symmetry for y=x^2+16x?

Write y=(x+8)^2-64. Vertex is (-8,-64). Axis is x=-8.

Answer

\(x^2+16x\) factors by taking out the greatest common factor \(x\):

\[
x^2+16x = x(x+16)
\]

Final result: \(\,x(x+16)\,\)

Detailed Explanation

We are asked to simplify the expression

\[
x^2 + 16x.
\]

Step 1: Check if the expression can be written in factored form.

Both terms \(x^2\) and \(16x\) contain a common factor of \(x\).

Step 2: Factor out the greatest common factor.

From \(x^2 + 16x\), the greatest common factor is \(x\). Factor \(x\) out:

\[
x^2 + 16x = x(x + 16).
\]

Final Answer:

\[
x^2 + 16x = x(x + 16).
\]

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Algebra FAQ

Factor the expression \(x^2+16x\).

\(x^2+16x=x(x+16)\).

What is the greatest common factor (GCF) of \(x^2+16x\)?

The GCF is \(x\), so the expression becomes \(x(x+16)\).

Find the zeros of \(x^2+16x=0\).

\(x(x+16)=0\) so \(x=0\) or \(x=-16\).

Solve \(x^2+16x=0\) by completing the square.

\(x^2+16x=(x+8)^2-64\). Set to zero: \((x+8)^2=64\) so \(x=-8\pm 8\), giving \(x=0,-16\).

Expand \(x(x+16)\) to check it matches \(x^2+16x\).

\(x(x+16)=x^2+16x\).

What are the vertex and axis of symmetry for \(y=x^2+16x\)?

Write \(y=(x+8)^2-64\). Vertex is \((-8,-64)\). Axis is \(x=-8\).

What is the value of \(x^2+16x\) when \(x=-4\)?

\((-4)^2+16(-4)=16-64=-48\).

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