Quick question about factoring. f(x)=2x^3 − 3x^2 −5x +6; k=1. K=1 is a factor. So I synthetically divide to get the new polynomial: 2x^2 - x- 6

My question is silly. When I set up to factor how do I know the order. (x )(2x ) or (2x )(x ) and more, if my terms are -3 and 2 how do I know which goes where without testing it all with FOIL

Question

Quick question about factoring. ​f(x)=2x^3 − 3x^2 −5x +​6; k=1. K=1 is a factor. So I synthetically divide to get the new polynomial: 2x^2 - x- 6

My question is silly. When I set up to factor how do I know the order. (x    )(2x    ) or (2x    )(x    ) and more, if my terms are -3 and 2 how do I know which goes where without testing it all with FOIL

simontheengineer · Answer

You can use a quadratic equation to find out your two values? 

This is usually what is done to find out two values for x.

anononion · Answer

well normally I look at the last number and find the factors that will add to the middle term, my question is how do I know which is written first, a -3 or 2 for example.

mathmale · Answer

The order in which you write your factors is immaterial.

mathmale · Answer

You are correct:  the quotient is 2x^2 - x- 6.

You can now apply synth. div. to finding the roots of 2x^2 - x- 6.

Write your 3 factors as (x-1)(x-?)(x+?).

You could check your work by multiplying out this expression.

watchmath · Answer

If you want you can do like this: First write $2x^2-x-6$ as $\frac{1}{2}\left((2x)^2-2x-12\right)$. Let $y=2x$, so you want to factor $\frac{1}{2} (y^2-y-12)=\frac{1}{2}(y+3)(y-4)=(2x+3)(x-2)$.