How do you factor 3x squared minus 3x minus 6?

Answer 1

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)

Answer 2

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

Answer 3

3x2 - 3x - 6 = 3(x2 - x - 2) = 3 (x + 1) (x - 2)

Answer 4

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)

Answer 5

(3x - 1)(x + 2)

Answer 6

3(x - 7)(x + 7)