🧠 Try This Practice Problem First
Created by volunteer coders Zhenchao Xia and Prof. Xin, Ke.
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📘 What Is the Trial and Error Method?
What are we doing?
We are factoring trinomials where the leading coefficient is not 1, using the trial and error method — not grouping.
We're looking for two binomials:
\((ax + m)(bx + n)\)
that multiply to give:
\(ax^2 + bx + c\)
How does it work?
Let’s try factoring:
\(6x^2 + 7x - 5\)
We’re looking for two binomials of the form:
\((_x + _)(_x + _)\)
- First terms must multiply to 6x² → try: (6x)(x), (3x)(2x)
- Last terms must multiply to -5 → try: ±1 and ±5
Try: \((3x - 1)(2x + 5)\)
- First: \(3x × 2x = 6x^2\)
- Outer: \(3x × 5 = 15x\)
- Inner: \(-1 × 2x = -2x\)
- Middle: \(15x - 2x = 13x\) ❌
Try: \((2x - 1)(3x + 5)\)
- First: \(2x × 3x = 6x^2\)
- Outer: \(2x × 5 = 10x\)
- Inner: \(-1 × 3x = -3x\)
- Middle: \(10x - 3x = 7x\) ✅
Final Answer: \((2x - 1)(3x + 5)\)
🎥 Watch This Video Explanation
Video created by Prof. Inkelis, Ellen as a volunteer.
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