Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
-(x+2)(x+3)
\]
Solution
1. Write the expression:
\[
-x^2 - 5x - 6
\]
2. Factor out \(-1\) from the entire expression:
\[
-\left( x^2 + 5x + 6 \right)
\]
3. Factor the quadratic \( x^2 + 5x + 6 \). We need two numbers that multiply to \( 6 \) and add to \( 5 \). The numbers \( 2 \) and \( 3 \) work because:
\[
2 \times 3 = 6 \quad \text{and} \quad 2 + 3 = 5
\]
4. Factor the quadratic:
\[
x^2 + 5x + 6 = (x+2)(x+3)
\]
5. Substitute back into the expression:
\[
-x^2 - 5x - 6 = -\left( (x+2)(x+3) \right)
\]
Final answer:
\[
-(x+2)(x+3)
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To factor the quadratic expression \(-x^{2}-5x-6\), we can start by factoring out \(-1\), giving us: \[ -(x^{2}+5x+6) \] Next, we look to factor the trinomial \(x^{2}+5x+6\). We need two numbers that multiply to \(6\) and add up to \(5\). The numbers \(2\) and \(3\) fit the bill, so we can factor the expression as: \[ -(x+2)(x+3) \] Thus, the fully factored form of the original expression is: \[ -(x+2)(x+3) \]
