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Algebra practice great for tutoring, Cheat Sheet of Algebra

Chamberlain College of NursingAlgebra

Use as a tool while tutoring or for preping yourself

Typology: Cheat Sheet

2025/2026

Uploaded on 04/06/2026

timika-henderson
timika-henderson 🇺🇸

2 documents

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Algebra Practice Sheet – Factoring & Rational Expressions
Section 1: Factoring Polynomials (1.5)
1. Greatest Common Factor (GCF)
Factor out the GCF from each polynomial:
2. 12x^3 + 18x^2
3. 8y^4 - 20y^3 + 12y^2
4. 15a^2b - 25ab^2 + 35ab
5. Trinomials with Leading Coefficient 1
Factor each trinomial:
6. x^2 + 7x + 12
7. y^2 - 5y + 6
8. a^2 + 9a + 20
9. Factoring by Grouping
Factor each polynomial by grouping:
10. x^3 + 3x^2 + 2x + 6
11. ab + ac + b^2 + bc
12. y^3 + 3y^2 - 4y - 12
13. Special Products
Perfect square trinomials:
14. x^2 + 6x + 9
15. 4y^2 - 12y + 9
Difference of squares:
12. x^2 - 16
13. 9a^2 - 25b^2
5. Sum and Difference of Cubes
Factor completely:
pf3

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Algebra Practice Sheet – Factoring & Rational Expressions Section 1: Factoring Polynomials (1.5)

  1. Greatest Common Factor (GCF) Factor out the GCF from each polynomial:
  2. 12x^3 + 18x^
  3. 8y^4 - 20y^3 + 12y^
  4. 15a^2b - 25ab^2 + 35ab
  5. Trinomials with Leading Coefficient 1 Factor each trinomial:
  6. x^2 + 7x + 12
  7. y^2 - 5y + 6
  8. a^2 + 9a + 20
  9. Factoring by Grouping Factor each polynomial by grouping:
  10. x^3 + 3x^2 + 2x + 6
  11. ab + ac + b^2 + bc
  12. y^3 + 3y^2 - 4y - 12
  13. Special Products Perfect square trinomials:
  14. x^2 + 6x + 9
  15. 4y^2 - 12y + 9 Difference of squares:
  16. x^2 - 16
  17. 9a^2 - 25b^
  18. Sum and Difference of Cubes Factor completely:
  1. x^3 + 27
  2. 8y^3 - 125
  3. 27a^3 + 64b^
  4. Polynomials with Fractional or Negative Exponents Factor out the GCF:
  5. x^{5/2} + x^{3/2}
  6. y^{-3} - 2y^{-5} Section 2: Rational Expressions (1.6)
  7. Simplify Simplify each rational expression:
  8. 6x^2 / 9x
  9. (x^2 - 9) / (x^2 - 6x + 9)
  10. (4y^2 - 16) / 2y
  11. Multiply Multiply and simplify:
  12. (x / (x+2)) * ((x+2) / (x^2 + 3x + 2))
  13. ((y^2 - 4) / y) * (y / (y+2))
  14. Divide Divide and simplify:
  15. ((x^2 - 1) / (x+3)) ÷ ((x-1) / (x+3))
  16. ((y^2 + 5y + 6) / (y+2)) ÷ ((y+3) / y)
  17. Add or Subtract Find a common denominator and simplify:
  18. 1/x + 2/x^
  19. y/(y-1) - 2/(y-1)
  20. a/(a+1) + 3/(a+1)
  21. Complex Rational Expressions