200 x 4 = 800
200 - 196 = 4
4 x 4 = 16
800 - 16 = 784
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1 x 196, 2 x 98, 4 x 49, 7 x 28, 14 x 14 = 196
2 x 2 x 7 = 28 2 x 7 x 7 = 98 2 x 2 x 7 x 7 = 196, the LCM
You're looking for factors of 196 that combine to make 28. If that's +196, the answer is (x - 14)(x - 14) or (x - 14)2 If that's -196, it gets ugly in a hurry.
Let's see in a prime factorization tree. 2, 98 2, 2, 49 2, 2, 7, 7. The answer is:2 to the power of 2 and 7 to the power of 2 ;/or 2 x 2 x 7 x 7
3xx-5883(xx-196)Factor (long):xx+0x-196axx+bx+ca=1b=0c=-196Multiply a and c:1*-196=-196Find multiples of ac that add up to b (d,e [ie de=ac, d+e=b]):-196=-1*2*2*7*7,-2*98, 2*-98-7*28, 7*-28-4*49, 4*-49-14*14,Rewrite axx+bx+c into axx+dx+ex+c:3(xx-14x+14x-196)Factor sets of terms (ie axx+dx, and ex+c):3(xx-14x+14x-196)3(x(x-14)+14(x-14))Combine like terms:3(x(x-14)+14(x-14))3(x-14)(x+14)Factor (short):3(xx+0x-196)Factors of -196, find which ones add up to 0-196=-1*2*2*7*7,-2*98, 2*-98-7*28, 7*-28-4*49, 4*-49-14*14,Rewrite in form of (x+d)(x+e)3(x+14)(x-14)Factor (shorter):-when a polynomial takes the form of xx-c, it can be factored into the form:(x+sqrt(c))(x-sqrt(c))sqrt(196)=14,-143(x+14)(x-14)