Factoring Quadratics Answer Key
Teacher Answer Key Factoring Trinomials (\(a = 1\))
Page 1 of 2
Factor each polynomial completely.
Complete Solutions & Factor Pairs
#1: \(x^2 + x - 42\)
Find two numbers that:
• Multiply to \(c = -42\)
• Add to \(b = 1\)
→ Pair: \(7\) and \(-6\) \(\; (7 \cdot -6 = -42,\; 7 - 6 = 1)\)
Answer: \((x + 7)(x - 6)\)
#2: \(x^2 + 3x - 28\)
Find two numbers that:
• Multiply to \(c = -28\)
• Add to \(b = 3\)
→ Pair: \(7\) and \(-4\) \(\; (7 \cdot -4 = -28,\; 7 - 4 = 3)\)
Answer: \((x + 7)(x - 4)\)
#3: \(x^2 - x - 72\)
Find two numbers that:
• Multiply to \(c = -72\)
• Add to \(b = -1\)
→ Pair: \(-9\) and \(8\) \(\; (-9 \cdot 8 = -72,\; -9 + 8 = -1)\)
Answer: \((x - 9)(x + 8)\)
#4: \(x^2 - 3x - 40\)
Find two numbers that:
• Multiply to \(c = -40\)
• Add to \(b = -3\)
→ Pair: \(-8\) and \(5\) \(\; (-8 \cdot 5 = -40,\; -8 + 5 = -3)\)
Answer: \((x - 8)(x + 5)\)
#5: \(x^2 + 2x - 35\)
Find two numbers that:
• Multiply to \(c = -35\)
• Add to \(b = 2\)
→ Pair: \(7\) and \(-5\) \(\; (7 \cdot -5 = -35,\; 7 - 5 = 2)\)
Answer: \((x + 7)(x - 5)\)
#6: \(x^2 - 5x - 24\)
Find two numbers that:
• Multiply to \(c = -24\)
• Add to \(b = -5\)
→ Pair: \(-8\) and \(3\) \(\; (-8 \cdot 3 = -24,\; -8 + 3 = -5)\)
Answer: \((x - 8)(x + 3)\)
Teacher Answer Key Factoring Trinomials (\(a = 1\))
Page 2 of 2
Factor each polynomial completely.
Complete Solutions & Factor Pairs
#7: \(x^2 + 8x + 15\)
Find two numbers that:
• Multiply to \(c = 15\)
• Add to \(b = 8\)
→ Pair: \(5\) and \(3\) \(\; (5 \cdot 3 = 15,\; 5 + 3 = 8)\)
Answer: \((x + 5)(x + 3)\)
#8: \(x^2 - 9x + 18\)
Find two numbers that:
• Multiply to \(c = 18\)
• Add to \(b = -9\)
→ Pair: \(-6\) and \(-3\) \(\; (-6 \cdot -3 = 18,\; -6 - 3 = -9)\)
Answer: \((x - 6)(x - 3)\)
#9: \(x^2 + 4x - 32\)
Find two numbers that:
• Multiply to \(c = -32\)
• Add to \(b = 4\)
→ Pair: \(8\) and \(-4\) \(\; (8 \cdot -4 = -32,\; 8 - 4 = 4)\)
Answer: \((x + 8)(x - 4)\)
#10: \(x^2 - 2x - 63\)
Find two numbers that:
• Multiply to \(c = -63\)
• Add to \(b = -2\)
→ Pair: \(-9\) and \(7\) \(\; (-9 \cdot 7 = -63,\; -9 + 7 = -2)\)
Answer: \((x - 9)(x + 7)\)
#11: \(x^2 - 4x - 45\)
Find two numbers that:
• Multiply to \(c = -45\)
• Add to \(b = -4\)
→ Pair: \(-9\) and \(5\) \(\; (-9 \cdot 5 = -45,\; -9 + 5 = -4)\)
Answer: \((x - 9)(x + 5)\)
#12: \(x^2 + 2x - 48\)
Find two numbers that:
• Multiply to \(c = -48\)
• Add to \(b = 2\)
→ Pair: \(8\) and \(-6\) \(\; (8 \cdot -6 = -48,\; 8 - 6 = 2)\)
Answer: \((x + 8)(x - 6)\)
