Algebra 1 Factoring Flashcards

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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.

(x+8)(x-2) Signup and view all the answers

Factor x² + 9x + 20.

(x+5)(x+4) Signup and view all the answers

Factor x² - 8x + 16.

(x-4)(x-4) Signup and view all the answers

Factor x² - 25.

(x-5)(x+5) Signup and view all the answers

Factor x² - 49.

(x-7)(x+7) Signup and view all the answers

Factor 4x² - 81.

(2x-9)(2x+9) Signup and view all the answers

Factor 2x² - 3x - 5.

(2x-5)(x+1) Signup and view all the answers

Factor 6x² - 13x - 5.

(3x+1)(2x-5) Signup and view all the answers

Factor 10x² + 11x + 3.

(2x+1)(5x+3) Signup and view all the answers

Factor ax - 3a + xy - 3y.

(x-3)(a+y) Signup and view all the answers

Factor ax + 5x + 2a + 10.

(x+2)(a+5) Signup and view all the answers

Factor 12x³ - 9x² + 15x.

3x(4x² - 3x + 5) Signup and view all the answers

Factor 30x² + 15x + 5.

5(6x² + 3x + 1) Signup and view all the answers

Factor 2x² + 9x + 10.

(2x+5)(x+2) Signup and view all the answers

Factor 5x² + 31x + 6.

(x+6)(5x+1) Signup and view all the answers

Factor x² + 10x + 16.

(x+2)(x+8) Signup and view all the answers

Factor x² - 11x + 24.

(x-3)(x-8) Signup and view all the answers

Factor x² - 1.

(x-1)(x+1) Signup and view all the answers

Factor x² - 36.

(x+6)(x-6) Signup and view all the answers

Factor 2x² + 20x + 32.

2(x+8)(x+2) Signup and view all the answers

Factor 4x² - 4.

4(x-1)(x+1) Signup and view all the answers

Factor 3x² + 2x - 16.

(3x+8)(x-2) Signup and view all the answers

Factor 3x² + 7x + 2.

(x+2)(3x+1) Signup and view all the answers

Factor 9x⁴ - 16y².

(3x²-4y)(3x²+4y) Signup and view all the answers

Factor 3x² - 27.

3(x+3)(x-3) Signup and view all the answers

Study Notes

Factoring Techniques in Algebra 1

Guess and Check Method: Used for factoring quadratics where the leading coefficient (a=1).
- Example: x² - 3x - 18 factors to (x-6)(x+3).
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).
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).
Grouping Method: Involves grouping terms to factor common elements.
- Example: ax - 3a + xy - 3y factors to (x - 3)(a + y).
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

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).
Factoring Special Forms:
- x² - 1 factors to (x - 1)(x + 1).
- x² - 36 factors to (x + 6)(x - 6).
Multiple Terms:
- 2x² + 9x + 10 factors to (2x + 5)(x + 2).
- 5x² + 31x + 6 factors to (x + 6)(5x + 1).
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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Description

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.