Question
Factor the given trinomial. If the trinomial cannot be factored, indicate "Not Factorable" \[ x^{2}-12 x+32 \]
Ask by Montgomery Thornton. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x^{2}-12x+32 = (x-8)(x-4) \)
Solution
Factor the expression \( x^{2}-12x+32 \).
Factor the expression by following steps:
- step0: Factor:
\(x^{2}-12x+32\)
- step1: Rewrite the expression:
\(x^{2}+\left(-4-8\right)x+32\)
- step2: Calculate:
\(x^{2}-4x-8x+32\)
- step3: Rewrite the expression:
\(x\times x-x\times 4-8x+8\times 4\)
- step4: Factor the expression:
\(x\left(x-4\right)-8\left(x-4\right)\)
- step5: Factor the expression:
\(\left(x-8\right)\left(x-4\right)\)
The given trinomial \(x^{2}-12x+32\) can be factored as \((x-8)(x-4)\).
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Simplify this solution Beyond the Answer
To factor the trinomial \( x^{2}-12x+32 \), we look for two numbers that multiply to \( 32 \) (the constant term) and add up to \( -12 \) (the coefficient of \( x \)). The numbers \( -4 \) and \( -8 \) fit the bill since \( -4 \times -8 = 32 \) and \( -4 + -8 = -12 \). So, we can rewrite the trinomial as: \[ (x - 4)(x - 8) \] In conclusion, the factored form of \( x^{2}-12x+32 \) is \( (x - 4)(x - 8) \).
