0
3xx-588
3(xx-196)
Factor (long):
xx+0x-196
axx+bx+c
a=1
b=0
c=-196
Multiply a and c:
1*-196=-196
Find 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,-14
3(x+14)(x-14)
That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: (0 plus or minus the square root of 30) divided by 3.
x = 1.8257418583505538
x = -1.8257418583505538
Since 3 squared is 9 and 9 - 9 equals 0, that's going to be tough to factor.
3x2 - 9 factors to 3(x2 - 3)
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