Practice with Factoring Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

 Factor completely: (While a specific method may be stated in the explanations, ANY method of solution is acceptable.)
 1. Choose: 4(s² - 4)(s² + 4) 4(s - 2)(s + 2)(s² + 4) 4(s - 4)(s + 4) (2s2 - 8) (2s2 + 8) Explanation Factor out common factor of 4. 4(s^4 - 16) Difference of perfect squares. 4(s² - 4)(s² + 4) Difference of perfect squares again. 4(s - 2)(s + 2)(s² + 4)

 2. Choose: (a4 - b2)(a4 + b2) (a2 - b)(a2 +b)(a4 + b2) (a2 - b)2 (a4 + b2) (a4 - b)(a4 +b)(a4 + b2) Explanation Each term is a perfect square. (a^4)² = a^8 (b²)² = b^4 Apply the Difference of Squares twice.

 3. Choose: 3(x + 4) (x - 2) 3(x + 3) (x - 4) 3(x - 4) (x + 2) 3(x - 3) (x + 4) Explanation Factor out the GCF of 3 3(x² - 2x + 8) Factor the trinomial 3(x - 4)(x + 2)

 4. Choose: 5(y + 1) (y - 4) 5(y - 1) (y + 4) 5y(y + 1) (y - 4) 5y(y - 1) (y + 4) Explanation Factor out the GCF of 5y 5y(y² + 3y - 4) Factor the trinomial 5y(y + 4)(y - 1)

 5. Choose: 2(2x + 2)(x - 2) 2(2x - 2) (x + 2) 2(2x + 1)(x - 4) 2(2x - 1)(x + 4) Explanation Factor out the GCF of 2 2(2x² - 7x - 4) Factor the trinomial 2(2x + 1)(x - 4)

 6. Choose: (2x - 1) (x + 1) (2x + 1) (x - 1) (2x - 1) (2x - 1) (x - 1) (x + 1) Explanation What are possible factors of 2x²?  Answer 2x and x. What are possible factors of -1?  Answer -1 and 1. Possible answers are: (2x-1)(x+1)   gives a middle term of +x. (2x+1)(x-1)  gives a middle term of -x.  YEA!

 7. Choose: (3x - 1) (x + 2) (3x + 1) (x + 1) (3x + 1) (x - 2) (2x + 1) (x - 2) Explanation What are possible factors of 3x²?  Answer 3x and x. What are possible factors of -2?  Answer -2 and 1 OR 2 and -1. Possible answers: (3x+2)(x-1)  gives a middle term of -x. (3x-1)(x+2)  gives a middle term of +5x. (3x-2)(x+1)  gives a middle term of +x. (3x+1)(x-2)  gives a middle term of -5x.  YEA!

 8. Choose: (5m - 6) (m + 1) (5m + 2) (m - 3) (5m - 1) (m + 6) (5m - 2) (m + 3) Explanation Factoring by Grouping: 5 • (-6) = -30 Factors of -30 which add to 13 are 15 and -2. 5m² + 15m - 2m - 6 (split the middle) (5m² + 15m) + (-2m - 6) (Group) 5m(m + 3) + -2(m + 3) (Factor each group) (m + 3) (5m - 2)

 9. Choose: (x + 6) (4x + 4) (4x + 4) (x + 6) 4(x + 2) (x + 3) 4(x + 1) (x + 6) Explanation First factor out the common factor of 4. 4(x² + 5x + 6) Now factor the trinomial. 4(x+2)(x+3)

 10. Choose: (5x - 4) (x + 5) (5x + 2) (x - 10) 5(x - 1) (x + 4) 5(x - 2) (x + 2) Explanation Factor Completely: First factor the common factor of 5. 5(x² - 4) Now factor the difference of two squares. 5(x-2)(x+2)

 Topic Index | Algebra2/Trig Index | Regents Exam Prep Center Created by Donna Roberts