  I've covered all the types of polynomial factoring a student will encounter in most high school math courses here. There are additional types that occasionally appear in Math 30 or Math 31, and of course in University math. One such type is the 'sum and difference of cubes'. The format for a polynomial that we'll factor looks like this: where An and Bn are perfect cubes. Here is an example of a perfect cube: 125x6y12 125 is the cube of 5. You need to be able to recognize numerical perfect cubes; you should recall memorizing these in grade 9 math, to make it easier to simplify cube roots in Math 10C. Variables with exponents are perfect cubes if the exponents are multiples of 3. So 125x6y12 is the cube of 5x2y4 Notice that the exponents were divided by 3 Now we're ready to factor a polynomial that is either a sum or difference of cubes. The first step is to memorize the pattern, just as you did for a 'difference of squares' in Math 10C.
Here is a simple example: 8x9 - z3 has cube roots 2x3 and z The factored form is (2x3 - z)((2x3)2 + 2x3·z + z2) which becomes (2x3 - z)(4x6 + 2x3·z + z2) Study this example and make sure you understand where every term came from. |