## aceace 3 years ago Is there a faster the way to solve polynomials then to use the long division method? If yes, how do you do it?

1. Yahoo!

Factorize

2. Hero

Synthetic Division

3. aceace

can you please show me how to do synthetic division? @Hero

4. Traxter

Factor by inspection. For example, say we had x^3 + 6x^2 + 11x +6. You could spot that (x+1) is a factor (substitute x=-1 to see this) and then write the semi-factorised verision by inspection: (x+1)(x^2+5x+6) And continue reducing and taking factors out until you get to (x+1)(x+2)(x+3). It's a bit odd to describe the method, but I'll explain the first step: I took out (x+1). We have x^3 so I know the first term in the second set of bracekets will have to be x^2. When this is multiplied by x+1 we get the x^3, but only get x^2 when we need 6x^2. So the next term in the second set of brackets will be 5x (since it will multiply with the x from the first set of brackets to give a total of 6x^2). So up till now we have (x+1)(x^2+5x+...). The 5x completed the x^2 terms, but only gives us 5x, when we need 11x. So our next term will be +6, to give the extra 6x and the +6. So at the end of this step we have (x+1)(x^2+5x+6). You can then factorise x^2+5x+6 easily. It seems long winded in the explanation but it really isn't, it's basically just shorthand long division. Please let me know if I can make something more clear.