Express the polynomial as a product of linear factors.
ƒ(x)=3x^3+12x^2+3x-18

A. (x+3)(x+6)(x-1)
B. 3(x-1)(x+3)(x+2)
C. (x-2)(x+3)(x-3)
D. (x-3)(x+3)(x-2)

Question

Express the polynomial as a product of linear factors.
ƒ(x)=3x^3+12x^2+3x-18

A. (x+3)(x+6)(x-1)
B. 3(x-1)(x+3)(x+2)
C. (x-2)(x+3)(x-3)
D. (x-3)(x+3)(x-2)

myininaya · Answer

f(1)=0
so x=1 is a zero
so x-1 is a factor

myininaya · Answer

1|  3   12    3    -18
  |         3    15   18
       ---------------
     3    15   18|   0

so another factor is 3x^2+15x+18
but we can factor this factor

anonymous · Answer

Answer=B

myininaya · Answer

right you can also factor out 3
so we would have 3(x-1)(x^2+5x+6)
=3(x-1)(x+2)(x+3)

anonymous · Answer

f(x)=3x^3+12x2+3x-18
the common factor is 3 - pull that out, you get
3(x^3+4x^2+x-6)
so,
3(x-1)(x+2)(x+3)
prove it...
3*2*-1=-6
3+2-1=4

anonymous · Answer

thanks!