Question
Factor the given trinomial. If the trinomial cannot be factored, indicate "Not Factorable". \[ x^{2}+4 x-12 \]
Ask by Salinas O'Quinn. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x^{2}+4x-12 = (x-2)(x+6) \)
Solution
Factor the expression \( x^{2}+4x-12 \).
Factor the expression by following steps:
- step0: Factor:
\(x^{2}+4x-12\)
- step1: Rewrite the expression:
\(x^{2}+\left(6-2\right)x-12\)
- step2: Calculate:
\(x^{2}+6x-2x-12\)
- step3: Rewrite the expression:
\(x\times x+x\times 6-2x-2\times 6\)
- step4: Factor the expression:
\(x\left(x+6\right)-2\left(x+6\right)\)
- step5: Factor the expression:
\(\left(x-2\right)\left(x+6\right)\)
The given trinomial \(x^{2}+4x-12\) can be factored as \((x-2)(x+6)\).
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Simplify this solution Extra Insights
To factor the trinomial \( x^{2}+4x-12 \), we are looking for two numbers that multiply to \(-12\) (the constant term) and add to \(4\) (the coefficient of the linear term). The numbers \(6\) and \(-2\) fit this requirement since \(6 \times -2 = -12\) and \(6 + (-2) = 4\). Thus, we can factor the trinomial as: \[ (x + 6)(x - 2) \] So the factored form of \( x^{2}+4x-12 \) is \( (x + 6)(x - 2) \).
