Factor: 2x2 - 8x3 + 3x. We will write the trinomial in descending powers of x and factor out the common factor, -x. It is easier to factor trinomials that have a positive leading coefficient. Write the trinomial in descending powers of x -8x3 + 2x2 + 3x and we factor out the negative of the GCF, which is -x. -3) -8x3 + 2x2 + 3x = -x 3 x x2 - 2x – We must now factor 8x2 - 2x - 3. Its factorization has the following form. (2×D)(4×O) Because 8x · x or 4x · 2x gives 8x². 8x or To fill in the blanks, we find two factors of the last term of the trinomial (-3) that will give a middle term of –-2x. Because the sign of the last term is negative, the signs within its binomial factors will be different. If we pick factors of 2x and 4x for the first terms and 1 and -3 for the last terms, we have the following. Outer: -6x (2x + 1)(4x - 3) -6x + 4x = -2x Inner: 4x which gives the correct middle term of -2x, so it is correct. 1)(5x x- 3) 8x2 - 2x - 3 = (2x + 1) We can now give the complete factorization. -x( 8x? - 2 -x(2x + 2x )(4x - 3) -8x3 + 2x2 + 3x =