how do i factor x^3+2x^2-5x-6?

Question

jim_thompson5910 · Answer

Hint: list out the possible rational roots and use synthetic division and the remainder theorem to find the factors

anonymous · Answer

ok.  i will try to rememeber  how to do that.  I am iin pre-calc now but need to do this and  havent had algebra II for a year and a half!

nurali · Answer

You can use factor theorem.
f(x) = x^3+2x^2-5x-6
f(-1) = -1+2+5-6 = 0
So, x+1 is a factor

Use synthetic division, 
x^3+2x^2-5x-6 = (x+1)(x^2+x-6) = (x+1)(x-2)(x+3) = 0

So, the solution is x = -1, 2, -3

jim_thompson5910 · Answer

they just want to factor (not find the roots), so the answer would just be (x+1)(x-2)(x+3)

anonymous · Answer

nice solve nurali

anonymous · Answer

$$\lim_{x \rightarrow 2}\frac{ x^{3}+2x^{2}-5x-6 }{ x^{3}-7x+6 }$$     was the original question

jim_thompson5910 · Answer

factor the denominator and see what cancels

then plug in x = 2 and simplify

anonymous · Answer

ok

anonymous · Answer

simply solve

anonymous · Answer

i forget how to do synthetic division?

jim_thompson5910 · Answer

this page may help http://www.purplemath.com/modules/synthdiv.htm

anonymous · Answer

how do i get the divisor for the numerator?

jim_thompson5910 · Answer

what do you mean

anonymous · Answer

for synthetic division

jim_thompson5910 · Answer

well the coefficients for the numerator are

1    2   -5    -6

is that what you're asking?

anonymous · Answer

i got that.  what do you put in the bracket in front of those numbers?

jim_thompson5910 · Answer

well if you know x+1 is a factor, then -1 is a root, so it would be -1

anonymous · Answer

thanks