Factoring by Grouping (Four-Term Polynomials)factoring by groupingbecause pairs of terms are grouped together to factor the entire polynomial. The goal with this method is to find a common binomial that can be factored1. Factor the GCF.Determine if there is a GCF among all terms in the original polynomial and factor it, if one exists.2. Group the terms.Group the polynomial into two pairs—the first two terms and the last two terms.3. Factor the GCF from each group.Factor the GCF from the first pair of terms and then from the second pair of terms.4. Factor the common binomial.If common binomials do not exist, GCFs were factored accurately, and the expression cannot be rearranged, you have a prime polynomial.Don’t forget to check the factors for accuracy by distributing.Factoring Trinomials by GroupingWhat you've discovered is that the product of the middle two terms equals the product of the first andlast terms. Also, the sum of the middle two terms equals the middle term of the trinomial.Now let's use these ideas to factor the trinomial 6x2− 11x + 3 by grouping.First, check the result of the Discriminant. From the equation a = 6, b = −11, and c = 3.b2− 4ac(−11)2− 4(6)(3)121 − 72491. Factor the GCF.Determine if there is a GCF among all terms in the original polynomial and factor it, if one exists.2. Split the middle term.Multiply the leading coefficient and the constant.Find factors of this product that sum to the middle coefficient.Rewrite the polynomial with those factors replacing the middle term.