To factor the quadratic equation \( x^2 - 10x + 21 = 0 \), we need to find two numbers that multiply to \( 21 \) (the constant term) and add up to \( -10 \) (the coefficient of the \( x \) term).

The two numbers that satisfy this condition are \( -7 \) and \( -3 \), because:

\[
-7 \times -3 = 21
\]
\[
-7 + -3 = -10
\]

Therefore, we can factor the quadratic equation as:

\[
(x - 7)(x - 3) = 0
\]

So the factored form of the equation is:

\[
(x - 7)(x - 3) = 0
\]

Would you like details or have any questions?

Here are some related questions:
1. How do you solve the quadratic equation after factoring it?
2. What are the solutions to the equation \( (x - 7)(x - 3) = 0 \)?
3. What are other methods to solve a quadratic equation, like completing the square?
4. How does the discriminant determine the number of solutions for a quadratic equation?
5. Can all quadratic equations be factored easily?

**Tip:** Always check your factored terms by expanding them back out to ensure they match the original equation.

Learn how to factor the quadratic equation x^2 - 10x + 21 with step-by-step instructions. This guide covers key algebraic concepts and the zero product property, making it ideal for students in Grades 8-10.

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