When we encounter polynomials that occur often, we can factor them quickly using patterns. We generally refer to this as special factoring. We will encounter perfect square trinomials, the difference of two squares, the difference of two cubes, and the sum of two cubes.
Test Objectives:•Demonstrate the ability to factor a perfect square trinomial from memory
•Demonstrate the ability to factor the difference of two squares from memory
•Demonstrate the ability to factor the sum/difference of two cubes from memory
Special Factoring Test:
#1:
Instructions: Factor each.
a) x^{2} - 25
b) x^{2} - 100
c) p^{2} - 1
#2:
Instructions: Factor each.
a) 8n^{3} - 18n
b) 3x^{2} + 36x + 108
#3:
Instructions: Factor each.
a) 49r^{2} - 84r + 36
b) 196n^{4} + 56n^{3} + 4n^{2}
#4:
Instructions: Factor each.
a) 7b^{2} - 70b + 175
b) 216u^{3} + 1
#5:
Instructions: Factor each.
a) 375x - 24x^{4}
b) 125nx^{6} + 64ny^{6}
Written Solutions:
Solution:
a) (x + 5)(x - 5)
b) (x + 10)(x - 10)
c) (p + 1)(p - 1)
Solution:
a) 2n(2n + 3)(2n - 3)
b) 3(x + 6)^{2}
Solution:
a) (7r - 6)^{2}
b) 4n^{2}(7n + 1)^{2}
Solution:
a) 7(b - 5)^{2}
b) (6u + 1)(36u^{2} - 6u + 1)
Solution:
a) 3x(5 - 2x)(25 + 10x + 4x^{2})
b) n(5x^{2} + 4y^{2})(25x^{4} - 20x^{2}y^{2} + 16y^{4})