Identify the greatest common factor, if there is one, of the trinomial 4x^2 + 6x + 2. A greatest common factor is the greatest number or product of a number and variable that can be divided into each term. The greatest common factor is 2.
Factor, or reduce, the trinomial by the greatest common factor by dividing each term by 2 and placing it outside the trinomial. This equals 2(2x^2 + 3x + 1).
Determine the pair of factors that equal the first term of the trinomial. The correct pair of factors is 2x and x because 2x times x equals 2x^2.
Place 2x and x in the first term of each the following binomials: (2x )(x ). Leave the second terms of each binomial blank.
Determine the possible factors, or pairs of numbers, whose product equals the last term in the trinomial. The possible pairs of factors of the last term are 1, 1 and -1, -1 -- because 1 x 1 = 1, and -1 x -1 = 1 as well.
Place each pair of factors of the last term in the second term of the binomials (2x )(x ). This gives the two possibilities (2x + 1)(x + 1) and (2x - 1)(x - 1).
Determine which pair of factors equals the trinomial when multiplied together using the FOIL method. (2x - 1)(x - 1) produces 2x^2 - 3x + 1, which is incorrect. The correct pair is (2x + 1)(x + 1). Including the 2 that was previously factored out, the factors of the trinomial are (2)(2x + 1)(x + 1).