Unboxing Trinomials Worksheet
Equation Unboxing
Name:
Factoring Trinomials: \(x^2 + bx + c\)
Assembly Guide
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- Identify \(b\) and \(c\) in the expression.
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- Find numbers that multiply to \(c\) and add to \(b\).
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- Write factors as: \( (x + p)(x + q) \).
Note: If \(c\) is negative, factors have opposite signs.
Example: \(x^2 + 7x + 10\)
• \(b = 7, c = 10\)
• Factors: 2 and 5
• \(2 + 5 = 7\)
Result: \((x + 2)(x + 5)\)
<table class="w-28 text-center text-[10px] border-collapse bg-white"><tbody><tr class="bg-slate-100 font-bold"><td class="border p-0.5">Mult</td><td class="border p-0.5">Add</td></tr><tr><td class="border p-0.5">1, 10</td><td class="border p-0.5 text-red-500">11</td></tr><tr class="font-bold text-indigo-600"><td class="border p-0.5">2, 5</td><td class="border p-0.5">7</td></tr></tbody></table>
The Assembly Line
01
\(x^2 + 8x + 12\)
Workspace
Final Factored Form:
02
\(x^2 + 5x + 6\)
Workspace
Final Factored Form:
03
\(x^2 - 7x + 12\)
Workspace
Final Factored Form:
04
\(x^2 - x - 20\)
Workspace
Final Factored Form:
05
\(x^2 + 3x - 10\)
Workspace
Final Factored Form:
Unboxing Trinomials Answer Key
Answer Key
Unboxing Trinomials
Problem 01
\(x^2 + 8x + 12\)
• Factors of 12: (2, 6)
• Sum: \(2 + 6 = 8\)
Result: \((x + 2)(x + 6)\)
Problem 02
\(x^2 + 5x + 6\)
• Factors of 6: (2, 3)
• Sum: \(2 + 3 = 5\)
Result: \((x + 2)(x + 3)\)
Problem 03
\(x^2 - 7x + 12\)
• Factors of 12: (-3, -4)
• Sum: \(-3 + (-4) = -7\)
Result: \((x - 3)(x - 4)\)
Problem 04
\(x^2 - x - 20\)
• Factors of -20: (-5, 4)
• Sum: \(-5 + 4 = -1\)
Result: \((x - 5)(x + 4)\)
Problem 05
\(x^2 + 3x - 10\)
• Factors of -10: (5, -2)
• Sum: \(5 + (-2) = 3\)
Result: \((x + 5)(x - 2)\)
Teacher Note: Ensure students check their work using FOIL distribution.
