## College Algebra (10th Edition)

LCM = $3(x-3)(x+3)(2x+5)$
Step 1: Factor each polynomial completely. $3x^{2}-27=3(x^{2}-9)$... recognize a difference of squares $=3(x-3)(x+3)$ $2x^{2}-x-15=...$ For $ax^{2}+bx+c$ we search for factors of ac whose sum is b, and rewrite the $bx$ term. $-6$ and $+5$ are such factors, $2x^{2}-x-15=2x^{2}-6x+5x-15=$ $=2x(x-3)+5(x-3)$ $=(2x+5)(x-3)$ Step 2: The LCM is the product of each of these factors raised to a power equal to the greatest number of times that the factor occurs in the polynomials. LCM = $3(x-3)(x+3)(2x+5)$