In many cases, we encounter the same type of polynomial over and over again. We can factor these frequently occurring polynomials very quickly using special factoring formulas. We memorize the formula generically, then use substitution to apply the formula to a real problem. Using these formulas will greatly improve speed on homework, tests, and standardized tests such as the ACT and SAT.

Test Objectives
• Demonstrate the ability to factor a perfect square trinomial
• Demonstrate the ability to factor the difference of two squares
• Demonstrate the ability to factor the sum/difference of cubes
Special Factoring Practice Test:

#1:

Instructions: Factor each.

$$a)\hspace{.2em}x^2 - 10x + 25$$

$$b)\hspace{.2em}x^2 - 4$$

#2:

Instructions: Factor each.

$$a)\hspace{.2em}128x^2 + 320x + 200$$

$$b)\hspace{.2em}24x^2 - 486$$

#3:

Instructions: Factor each.

$$a)\hspace{.2em}1440x^2a - 1690a$$

$$b)\hspace{.2em}432x^2 + 504x + 147$$

#4:

Instructions: Factor each.

$$a)\hspace{.2em}8x^3 - 27$$

$$b)\hspace{.2em}128x^3 + 2y^3$$

#5:

Instructions: Factor each.

$$a)\hspace{.2em}x^2 - 6x + 9 - y^4$$

$$b)\hspace{.2em}y^2 - x^2 + 6x - 9$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}(x-5)^2$$

$$b)\hspace{.2em}(x+2)(x-2)$$

#2:

Solutions:

$$a)\hspace{.2em}8(4x+5)^2$$

$$b)\hspace{.2em}6(2x+9)(2x - 9)$$

#3:

Solutions:

$$a)\hspace{.2em}10a(12x + 13)(12x - 13)$$

$$b)\hspace{.2em}3(12x + 7)^2$$

#4:

Solutions:

$$a)\hspace{.2em}(2x - 3)(4x^2 + 6x + 9)$$

$$b)\hspace{.2em}2(4x + y)(16x^2 - 4xy + y^2)$$

#5:

Solutions:

$$a)\hspace{.2em}(x - 3 + y^2)(x - 3 - y^2)$$

$$b)\hspace{.2em}(y + x - 3)(y - x + 3)$$