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\( x^{2} + 8x + 12 = (x + 2)(x + 6) \)
Solución
1. We start with the quadratic expression:
\[
x^{2} + 8x + 12
\]
2. To factor, we need to find two numbers that multiply to \(12\) (the constant term) and add up to \(8\) (the coefficient of \(x\)).
3. The two numbers are \(2\) and \(6\) because:
\[
2 \times 6 = 12 \quad \text{and} \quad 2 + 6 = 8
\]
4. Therefore, we can express the quadratic as:
\[
x^{2} + 8x + 12 = (x + 2)(x + 6)
\]
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Simplifique esta solución Beyond the Answer
To solve the quadratic equation \( x^{2}+8x+12 \), you can factor it. Look for two numbers that multiply to 12 and add to 8. Those numbers are 6 and 2, allowing us to rewrite the equation as \( (x+6)(x+2) = 0 \). Setting each factor to zero gives us the solutions: \( x = -6 \) and \( x = -2 \). If you're plotting this on a graph, the parabola opens upwards, and its vertex is the lowest point. It intersects the x-axis at the points we found, -6 and -2, while the vertex can be calculated using the formula \( -b/(2a) \), which yields \( -4 \) for x and substituting back gives the vertex's y-value.
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