Factoring ax²+bx+c by grouping has some similarity to factoring into two binomials, but grouping works better when a and c are both not equal to 1. The factoring becomes more intricate when there are two constants to factor separately.Continue Reading
Both the terms ac and a+c are required. As a simple example, 6x²+7x+1 shows ac = 6 and a+c = 7.
In this case, 6 can factor into 6x1 or 3x2.
If ac is positive, both terms are positive or negative based on the sign of b. If it is negative, one term is positive while the other is negative in order to equal b. In the example, 6x1 = 7, so this is the factor pair that is desired.
So, 6x²+7x+1 = 6x²+6x+x+1. Sometimes, the middle terms must be reversed to find the best match for the next step.
Now 6x²+6x+x+1 = 6x(x+1)+1(x+1). The final step is factoring the binomial (x+1) from each term, giving (6x+1)(x+1) as the final answer.