About Special Factoring:
When factoring, we often come across the same types of polynomials repeatedly. Special factoring formulas allow us to factor these types of polynomials very quickly. By memorizing the formulas and applying substitution, you can obtain an immediate answer without going through the normal factoring steps. We will encounter perfect square trinomials, the difference of squares, and the sum/difference of cubes.
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
#1:
Instructions: Factor each using special factoring formulas.
$$a)\hspace{.2em}x^2 - 10x + 25$$
$$b)\hspace{.2em}x^2 - 4$$
Watch the Step by Step Video Solution View the Written Solution
#2:
Instructions: Factor each using special factoring formulas.
$$a)\hspace{.2em}128x^2 + 320x + 200$$
$$b)\hspace{.2em}24x^2 - 486$$
Watch the Step by Step Video Solution View the Written Solution
#3:
Instructions: Factor each using special factoring formulas.
$$a)\hspace{.2em}1440x^2a - 1690a$$
$$b)\hspace{.2em}432x^2 + 504x + 147$$
Watch the Step by Step Video Solution View the Written Solution
#4:
Instructions: Factor each using special factoring formulas.
$$a)\hspace{.2em}8x^3 - 27$$
$$b)\hspace{.2em}128x^3 + 2y^3$$
Watch the Step by Step Video Solution View the Written Solution
#5:
Instructions: Factor each using special factoring formulas.
$$a)\hspace{.2em}x^2 - 6x + 9 - y^4$$
$$b)\hspace{.2em}y^2 - x^2 + 6x - 9$$
Watch the Step by Step Video Solution View the Written Solution
Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}(x-5)^2$$
$$b)\hspace{.2em}(x+2)(x-2)$$
Watch the Step by Step Video Solution
#2:
Solutions:
$$a)\hspace{.2em}8(4x+5)^2$$
$$b)\hspace{.2em}6(2x+9)(2x - 9)$$
Watch the Step by Step Video Solution
#3:
Solutions:
$$a)\hspace{.2em}10a(12x + 13)(12x - 13)$$
$$b)\hspace{.2em}3(12x + 7)^2$$
Watch the Step by Step Video Solution
#4:
Solutions:
$$a)\hspace{.2em}(2x - 3)(4x^2 + 6x + 9)$$
$$b)\hspace{.2em}2(4x + y)(16x^2 - 4xy + y^2)$$
Watch the Step by Step Video Solution
#5:
Solutions:
$$a)\hspace{.2em}(x - 3 + y^2)(x - 3 - y^2)$$
$$b)\hspace{.2em}(y + x - 3)(y - x + 3)$$
