https://file.aiquickdraw.com/mathbot/file/1725413574089suenplou.jpg

The expression in the image is \( x^2 + x - 12 \). To factor this quadratic expression, we need to find two numbers that multiply to \(-12\) (the constant term) and add to \(1\) (the coefficient of the linear term \(x\)).

The two numbers that satisfy these conditions are \(4\) and \(-3\), because:

\[
4 \times (-3) = -12
\]
\[
4 + (-3) = 1
\]

Therefore, the factorization of \( x^2 + x - 12 \) is:

\[
(x + 4)(x - 3)
\]

Would you like more details or have any questions about this factorization?

Here are 5 related questions for further practice:

1. How would you factor \( x^2 - 5x + 6 \)?
2. What are the roots of the equation \( x^2 + x - 12 = 0 \)?
3. How can you use the quadratic formula to verify the factors of \( x^2 + x - 12 \)?
4. What is the relationship between the coefficients and the roots of a quadratic equation?
5. How can you factor a quadratic expression if the leading coefficient is not 1?

**Tip:** Always check your factors by multiplying them back together to ensure you get the original expression.

Find the factors of the quadratic expression x^2 + x - 12.

Learn how to factor the quadratic expression x^2 + x - 12 with a step-by-step solution. This algebra problem involves key concepts like factoring and quadratic equations, ideal for students in Grades 7-9.

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