Q. \(x^2 – 9\)

Q: Solve x^2-9=0.

Factor: (x-3)(x+3)=0. So x=3 or x=-3.

Q: Factor x^2-9.

Difference of squares: x^2-9=x^2-3^2=(x-3)(x+3).

Q: Find the roots of x^2-9 (where it equals zero).

Set x^2-9=0\Rightarrow x^2=9\Rightarrow x=\pm 3.

Q: What is the vertex of y=x^2-9?

It’s a parabola opening up. Vertex at x=0, y=-9, so (0,-9).

Q: Determine the y-intercept of y=x^2-9.

Plug x=0: y=0^2-9=-9. Intercept is (0,-9).

Q: Solve x^2-9=16.

x^2=25\Rightarrow x=\pm 5. So x=5 or x=-5.

Answer

We want to interpret “\(x^2-9\)”. It can be factored as a difference of squares.

\[
x^2-9 = x^2-3^2 = (x-3)(x+3).
\]

Final result: \(x^2-9 = (x-3)(x+3)\).

Detailed Explanation

Step 1: Understand the problem.

The expression given is

\[
x^2 – 9
\]

This is already a simplified polynomial expression. There is nothing to solve for (no equation equal to zero is provided), so the task is typically to rewrite/simplify it in a more useful form.

Step 2: Factor the expression (optional, but usually expected).

Recognize that \(x^2 – 9\) is a difference of squares, because \(9\) is a perfect square:

\[
x^2 – 9 = x^2 – 3^2
\]

Use the difference of squares formula:

\[
a^2 – b^2 = (a-b)(a+b)
\]

Here, identify \(a = x\) and \(b = 3\). Substitute into the formula:

\[
x^2 – 3^2 = (x-3)(x+3)
\]

So the factored form is

\[
x^2 – 9 = (x-3)(x+3)
\]

Final Answer:

\[
x^2 – 9 = (x-3)(x+3)
\]

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Algebra FAQ

Solve \(x^2-9=0\).

Factor: \((x-3)(x+3)=0\). So \(x=3\) or \(x=-3\).

Factor \(x^2-9\).

Difference of squares: \(x^2-9=x^2-3^2=(x-3)(x+3)\).

Find the roots of \(x^2-9\) (where it equals zero).

Set \(x^2-9=0\Rightarrow x^2=9\Rightarrow x=\pm 3\).

What is the vertex of \(y=x^2-9\)?

It’s a parabola opening up. Vertex at \(x=0\), \(y=-9\), so \((0,-9)\).

Determine the \(y\)-intercept of \(y=x^2-9\).

Plug \(x=0\): \(y=0^2-9=-9\). Intercept is \((0,-9)\).

Solve \(x^2-9=16\).

\(x^2=25\Rightarrow x=\pm 5\). So \(x=5\) or \(x=-5\).

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