Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.4 - Factoring Trinomials of the Form ax^2+bx+c - Problem Set 6.4 - Page 261: 41

In order to do factoring when the first coefficient is not one, we must use some trial and error. After all, when considering the factor $(ax +b)(cx +d)$, a and c are no longer simply one. Thus, in addition to considering all of the factors of the constant term (the term that is not multiplied by a variable), we must consider the factors of the coefficient for the squared term. Using all of these factors, it is then just a matter of doing trial and error until one of the combinations of factors multiplies to get the correct answer, which must multiply out to get the original expression. To check our answer, we can use the FOIL method to multiply these two factors together. To use the FOIL method, we multiply the first term from each binomial, the first term from the first binomial and the last term from the second binomial, the last term of the first binomial and the first term of the second binomial, and the last terms of each binomial. We then find the sum of these products and combine the like terms to get our answer.

In order to do factoring when the first coefficient is not one, we must use some trial and error. After all, when considering the factor $(ax +b)(cx +d)$, a and c are no longer simply one. Thus, in addition to considering all of the factors of the constant term (the term that is not multiplied by a variable), we must consider the factors of the coefficient for the squared term. Using all of these factors, it is then just a matter of doing trial and error until one of the combinations of factors multiplies to get the correct answer, which must multiply out to get the original expression. To check our answer, we can use the FOIL method to multiply these two factors together. To use the FOIL method, we multiply the first term from each binomial, the first term from the first binomial and the last term from the second binomial, the last term of the first binomial and the first term of the second binomial, and the last terms of each binomial. We then find the sum of these products and combine the like terms to get our answer.