# Chapter 6 - Section 6.3 - Factoring Trinomials Whose Leading Coefficient is Not 1 - Exercise Set - Page 444: 42

$(3x-2)(5x-3)$

#### Work Step by Step

Factoring by grouping: 1. Multiply the leading coefficient, a, and the constant, c. 2. Find the factors of ac whose sum is b. 3. Rewrite the middle term, bx, as a sum or difference using the factors from step 2. 4. Factor by grouping --- $15x^{2}-19x+6 =...$ Always start by searching for a GCF ... (there are none other than 1). 1. $\quad ac=+90$ 2. $\quad$sum = $-19\quad$... factors: $-10$ and $-9$ 3. $\quad$ $15x^{2}-19x+6 = (15x^{2}-10x)+(-9x+6 )$ 4. $\quad$... $= 5x(3x-2)+(-3)(3x-2) =(3x-2)(5x-3)$ Check by FOIL $F:\quad 15x^{2}$ $O:\quad -9x$ $I:\quad -10x$ $L:\quad +6$ $(3x-2)(5x-3)$ = $15x^{2}-19x+6$

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