Questions and Answers
Factor x² - 3x - 18.
(x-6)(x+3)
Factor x² + 5x + 6.
(x+2)(x+3)
Factor x² - 7x + 12.
(x-3)(x-4)
Factor x² + 6x - 16.
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Factor x² + 9x + 20.
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Factor x² - 8x + 16.
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Factor x² - 25.
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Factor x² - 49.
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Factor 4x² - 81.
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Factor 2x² - 3x - 5.
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Factor 6x² - 13x - 5.
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Factor 10x² + 11x + 3.
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Factor ax - 3a + xy - 3y.
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Factor ax + 5x + 2a + 10.
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Factor 12x³ - 9x² + 15x.
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Factor 30x² + 15x + 5.
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Factor 2x² + 9x + 10.
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Factor 5x² + 31x + 6.
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Factor x² + 10x + 16.
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Factor x² - 11x + 24.
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Factor x² - 1.
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Factor x² - 36.
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Factor 2x² + 20x + 32.
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Factor 4x² - 4.
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Factor 3x² + 2x - 16.
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Factor 3x² + 7x + 2.
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Factor 9x⁴ - 16y².
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Factor 3x² - 27.
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Study Notes
Factoring Techniques in Algebra 1
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Guess and Check Method: Used for factoring quadratics where the leading coefficient (a=1).
- Example: x² - 3x - 18 factors to (x-6)(x+3).
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Difference of Squares: A technique for factoring expressions of the form (a² - b²).
- Example: x² - 25 factors to (x - 5)(x + 5).
- Example: 4x² - 81 factors to (2x - 9)(2x + 9).
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AC Method (Split and Group): Suitable for quadratics with a leading coefficient other than 1.
- Factors using the product of (a) and (c) to split the middle term.
- Example: 2x² - 3x - 5 factors to (2x - 5)(x + 1).
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Grouping Method: Involves grouping terms to factor common elements.
- Example: ax - 3a + xy - 3y factors to (x - 3)(a + y).
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Greatest Common Factor (GCF): Identifying and factoring out the highest common factor.
- Example: 12x³ - 9x² + 15x factors to 3x(4x² - 3x + 5).
- Example: 30x² + 15x + 5 factors to 5(6x² + 3x + 1).
Important Factoring Examples
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Basic Quadratic Factoring:
- x² + 5x + 6 factors to (x + 2)(x + 3).
- x² - 7x + 12 factors to (x - 3)(x - 4).
- x² + 6x - 16 factors to (x + 8)(x - 2).
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Factoring Special Forms:
- x² - 1 factors to (x - 1)(x + 1).
- x² - 36 factors to (x + 6)(x - 6).
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Multiple Terms:
- 2x² + 9x + 10 factors to (2x + 5)(x + 2).
- 5x² + 31x + 6 factors to (x + 6)(5x + 1).
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Higher Degree Factoring:
- 9x⁴ - 16y² factors to (3x² - 4y)(3x² + 4y).
Review Tips
- Always look for the simplest factoring method first.
- Practice using each method with various polynomial forms to reinforce understanding.
- Break down complicated expressions by rearranging or adjacent grouping.
- Checking by expanding factors to confirm correctness prevents error.
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Test your knowledge on factoring polynomials with these flashcards. Each card provides a quadratic expression for you to factor using the guess and check method. Perfect for reinforcing your skills in Algebra 1.