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algebra · worked example

Solve x² + 7x + 12

Method: 整數因式分解. Verified step-by-step solution with our free AI math solver.
Problem

x2+7x+12x^2 + 7x + 12

Step-by-step solution

  1. 找出兩個數，使其相乘為 1212 且相加為 77。

  2. 列出 1212 的因數對：(1,12),(2,6),(3,4)(1, 12), (2, 6), (3, 4)。數對 (3,4)(3, 4) 相加為 77。✓

  3. 寫出因式分解後的形式：(x+3)(x+4)(x + 3)(x + 4)。

  4. 用展開驗證：(x+3)(x+4)=x2+4x+3x+12=x2+7x+12(x+3)(x+4) = x^2 + 4x + 3x + 12 = x^2 + 7x + 12。✓

Answer

(x+3)(x+4)(x + 3)(x + 4)

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