# Chapter 4 Quadratic Functions and Factoring - 4.4 Solve ax(squared) + bx + c = 0 by Factoring - 4.4 Exercises - Skill Practice - Page 263: 42

1, 5/3

#### Work Step by Step

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. Note, when the problem asks us to put it into intercept form, this is the same as asking us to factor the expression. We factor and set the factors equal to zero to find: $$(3x−5)(x−1) \\ x=1,5/3$$

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