https://file.aiquickdraw.com/mathbot/file/17254147375050qtcidit.jpg

The expression given in the image is:

\[
x^2 - 7x + 12
\]

To factor this quadratic expression, we need to find two numbers that multiply to \(12\) (the constant term) and add up to \(-7\) (the coefficient of the linear term).

These two numbers are \(-3\) and \(-4\), because:

\[
-3 \times -4 = 12 \quad \text{and} \quad -3 + (-4) = -7
\]

So, we can factor the quadratic as:

\[
x^2 - 7x + 12 = (x - 3)(x - 4)
\]

The factored form of \(x^2 - 7x + 12\) is \((x - 3)(x - 4)\).

Would you like more details or have any questions? Here are some related questions:

1. How can you confirm the factorization by expanding the factors?
2. What method is used to factor quadratic expressions like this one?
3. How would you solve \(x^2 - 7x + 12 = 0\) using the factored form?
4. What is the significance of the roots of the equation \(x^2 - 7x + 12 = 0\)?
5. How does the discriminant help in determining the type of roots a quadratic equation has?

**Tip:** When factoring quadratics, always check your factors by expanding them to ensure they match the original expression.

Find factor of the quadratic expression: x^2 - 7x + 12

Learn how to factor the quadratic expression x^2 - 7x + 12 with a step-by-step solution. This problem covers key algebraic concepts such as factoring and the zero product property, making it suitable for students in Grades 8-10.

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