Question

Factor completely, given that (x-2) is a factor.
y=x^3-12x^2+36x-32
Please show work!!! Thanks!

Answer 1

ok you know it has to look like
\[(x-2)(\text{something})\] right? and you can find the "something" by dividing

Answer 2

or you can find the "something" by thinking
has to look like
\[(x-2)(x^2+bx-16)\]

Answer 3

actually it has to look like
\[(x-2)(x^2+bx+16)\]since
\[-2\times 16=-32\]

Answer 4

b can be found easy enough since
\[-2x^2+bx^2=-12x^2\]
\[-2+b=-12\]
\[b=-10\]

Answer 5

or if you prefer you could start again with
\[(x-2)(x^2+bx+16)\]and then think that
\[-2bx+16x=36x\]
\[-2b+16=36\]
\[-2b=20\]
\[b=-10\] either way, doesn't matter which you use

Answer 6

Thank you :) When it comes to math, i have no idea what to do... O_o
lol