Factor the trinomial completely. x3+2x2−3x
To begin, the first two terms and the last two terms are grouped. This can be done using parentheses. y=2x3−x2+6x−3=(2x3−x2)+(6x−3)
In the first pair, factor out the GCF. Here, the GCF is x2. (2x3−x2)+(6x−3)x2(2x−1)+(6x−3) For the second pair, the GCF is 3. x2(2x−1)+(6x−3)x2(2x−1)+3(2x−1)
If the polynomial is factorable, this should lead to a sum of two terms with a common factor. In this case, that factor is (2x−1). x2(2x−1)+3(2x−1) (2x−1)(x2+3) This means that y=2x3−x2+6x−3 can be written as y=(2x−1)(x2+3).