Question
Factor the expression. \( x^{2}-12 x-28 \) \( x^{2}-12 x-28=\square \) (Type your answer in factored form.)
Ask by Nichols Edwards. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x^{2} - 12x - 28 = (x - 14)(x + 2) \)
Solution
1. We need to factor \( x^2 - 12x - 28 \).
2. Look for two numbers that multiply to \(-28\) (the constant term) and add to \(-12\) (the coefficient of \( x \)).
3. The two numbers are \(-14\) and \(2\) since:
\[
(-14) \times 2 = -28 \quad \text{and} \quad (-14) + 2 = -12.
\]
4. Therefore, we factor the quadratic as:
\[
x^2 - 12x - 28 = (x - 14)(x + 2).
\]
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Mind Expander
To factor the expression \( x^{2}-12x-28 \), we need to find two numbers that multiply to \(-28\) (the constant term) and add to \(-12\) (the coefficient of the linear term). The numbers that work are \(-14\) and \(2\). Thus, we can write: \[ x^{2}-12x-28 = (x - 14)(x + 2) \] So the factored form is \( (x - 14)(x + 2) \).