Q. \(x^2 + 18x\)

Q: Find the zeros of x^2+18x.

Set x(x+18)=0. Then x=0 or x=-18.

Q: Solve x^2+18x=0.

Same equation: x(x+18)=0. Solutions are x=0 and x=-18.

Q: Express x^2+18x in vertex form.

Complete the square: x^2+18x=(x+9)^2-81.

Q: Determine the axis of symmetry for y=x^2+18x.

From (x+9)^2-81, the axis is x=-9.

Q: What is the minimum value of y=x^2+18x.

Since the parabola opens up, minimum is at x=-9: y_{\min}=-81.

Answer

To factor \(x^2+18x\), take out the common factor \(x\):

\[
x^2+18x=x(x+18)
\]

Final result: \(x(x+18)\).

Detailed Explanation

We are given the expression \(x^2 + 18x\). The goal is to simplify or rewrite it appropriately. A common and useful step is to factor the expression.

Step 1: Identify the common factor

\(x^2 + 18x\) has a factor of \(x\) in both terms:

\(x^2 = x\cdot x\) and \(18x = x\cdot 18\).

Step 2: Factor out \(x\)

Because \(x\) is common, factor it out:

\[
x^2 + 18x = x(x + 18).
\]

Final Answer

\[
x^2 + 18x = x(x + 18).
\]

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Algebra FAQ

Factor \(x^2+18x\).

\(x^2+18x=x(x+18)\).

Find the zeros of \(x^2+18x\).

Set \(x(x+18)=0\). Then \(x=0\) or \(x=-18\).

Solve \(x^2+18x=0\).

Same equation: \(x(x+18)=0\). Solutions are \(x=0\) and \(x=-18\).

Express \(x^2+18x\) in vertex form.

Complete the square: \(x^2+18x=(x+9)^2-81\).

Determine the axis of symmetry for \(y=x^2+18x\).

From \((x+9)^2-81\), the axis is \(x=-9\).

What is the minimum value of \(y=x^2+18x\).

Since the parabola opens up, minimum is at \(x=-9\): \(y_{\min}=-81\).

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