MATH 095 Lecture Notes - Lecture 5: Greatest Common Divisor, Talking Lifestyle 1278
5 Apr 2017
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To factor something is to write it as a product (multiply) of two or more things. 72 = 2 x 2 x 2 x 3 x 3 (23 x 32) (cid:862)factored i(cid:374)to pri(cid:373)es(cid:863) (cid:862)factored completely. Gcf of 2 numbers is the largest # that divides both. Lcm of 2 numbers is smallest # that multiplies both. Examples x2-1 = (x)2 (1)2 (x+1)(x-1) t2-4 = (t)2 (2)2 (t+2)(t-2) 9a2-16b2 = (3a)2 (4b)2 = (3a+4b)(3a-4b) 3xy2(2x+3y)(2x-3y) x4-y4 = (x2)2 (y2)2 (x2+y2)(x2-y2) (x2+y2)(x+y)(x-y) If we multiply non-zero quantities, we get a non-zero product: if the product is zero, then at least one of the factors is zero. So from (x+3)(x-2)=0, we can conclude that x+3=0 or x-2=0. x = -3 or 2. Notice x2+x-6=0: most people try x2=6-x (cid:1876)(cid:2870)= (cid:888) (cid:1876); not helpful. So, we can solve equations by factoring. 4x-5=0: rational expressions (day 10) (cid:1876)=(cid:882),(cid:886)(cid:885),(cid:887)(cid:886) (cid:883)(cid:884),(cid:885)(cid:889), (cid:887)(cid:883)(cid:886),(cid:883)(cid:889)(cid:888) (cid:1853)(cid:1854) (cid:1853),(cid:1854) (cid:1853)(cid:1870)(cid:1857) (cid:1872)(cid:1857)(cid:1859)(cid:1857)(cid:1870)(cid:1871) & (cid:1854) (cid:882)
