Factoring Quadratic Expressions, Exercises of Mathematics

The steps to factor quadratic expressions by finding the common factors (cmf/gcf), completing the factors, and identifying the coefficients and signs of the terms. The examples given include factoring 15x²y + 20xy², 24a⁷b⁸ - 9a⁸b⁶ - 6a⁷b⁷, b⁴ - 64, 4x² - 49, x² + 4x + 4, and 9p² - 24p + 16.

Typology: Exercises

2021/2022

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1. 15x²y + 20xy²
CMF/GCF: 5xy 1st Term: 3x 2nd Term: 4y
Complete Factors: 5xy (3x + 4y)
2. 24a⁷b⁸ - 9a⁸b⁶ - 6a⁷b⁷
CMF/GCF: 3a⁷b⁶ 1st Term: 8b² 2nd Term: -3a 3rd Term: -2b
Complete Factors: 3a⁷b⁶ (8b² - 3a - 2b)
3. b⁴ - 64
Solution: Factors of 1st Term: b² • b² Factors of 2nd Term: -8 • 8
Complete Factors: (b² + 8)(b² - 8)
4. 4x² - 49
Solution: Factors of 1st Term: 2x • 2x Factors of 2nd Term: -7 • 7
5. x² + 4x + 4
Factors of the 1st Term: x • x Factors of the Last Term : 2 • 2
Sign of the Middle Term: +
Complete Factors: (x + 2)²
6. 9p² - 24p + 16
Factors of the 1st Term: 3p • 3p Factors of the Last Term : 4 • 4
Sign of the Middle Term: -
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  1. 15x²y + 20xy² CMF/GCF: 5xy 1st Term: 3x 2nd Term: 4y Complete Factors: 5xy (3x + 4y)
  2. 24a⁷b⁸ - 9a⁸b⁶ - 6a⁷b⁷ CMF/GCF: 3a⁷b⁶ 1st Term: 8b² 2nd Term: -3a 3rd Term: -2b Complete Factors: 3a⁷b⁶ (8b² - 3a - 2b)
  3. b⁴ - 64 Solution: Factors of 1st Term: b² • b² Factors of 2nd Term: -8 • 8 Complete Factors: (b² + 8)(b² - 8)
  4. 4x² - 49 Solution: Factors of 1st Term: 2x • 2x Factors of 2nd Term: -7 • 7
  5. x² + 4x + 4 Factors of the 1st Term: x • x Factors of the Last Term : 2 • 2 Sign of the Middle Term: + Complete Factors: (x + 2)²
  6. 9p² - 24p + 16 Factors of the 1st Term: 3p • 3p Factors of the Last Term : 4 • 4 Sign of the Middle Term: -