SOLUTION: How do i factor {{{x^3+3x^2-18x-40}}}

Algebra.Com
Question 288189: How do i factor
Found 2 solutions by richwmiller, AnlytcPhil:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
(x-4)*(x+2)*(x+5)
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
How do i factor

Since the leading coefficient is 1, if there
are any rational zeros, they will all be
± the integer factor of the absolute value of the
numerical term -40.  So if there are any, they will
be among these:

±1,±2,±4,±5,±8,±10,±20

We begin by trying +1 using synthetic division:

1 | 1  3  -18  -40
  |    1    4  -14
    1  4  -14  -54

So, 1 is not a zero, and so x-1 is not a factor.

We try -1:

-1 | 1  3 -18  -40
   |   -1  -2   20
     1  2 -20  -20

So, -1 is not a zero, and so x+1 is not a factor.

We try +2:

2 | 1  3 -18  -40
  |    2  10  -16
    1  5  -8  -56

So, 2 is not a zero, and so x-2 is not a factor.

We try -2:

-2 | 1  3 -18  -40
   |   -2  -2   40
     1  1 -20    0

Eureka!  We get a 0 remainder, so x+2 is a factor.
An the numbers on the bottom row of the synthetic
division left of the remainder 0 tell us the other
factor.  So we have now factored



as



Now we can factor the trinomial in
the second parentheses and we have the
complete factorization as:



Edwin

RELATED QUESTIONS

Factor: x^3 - 3x^2... (answered by tutorcecilia)
Factor: x^3 - 3x^2 -... (answered by checkley77)
I am to factor by grouping the following 3x^3+18x^2-5x -25 unsure how to do it (answered by josgarithmetic)
How do you factor... (answered by checkley77)
Factor the polynomial f(x). The solve the equation f(x)=0. {{{f(x)=x^3-3x^2-18x+40}}} (answered by Fombitz)
How do I factor... (answered by jim_thompson5910)
I need to factor... (answered by stanbon)
How do I factor this expression? {{{ 27x^2-18x... (answered by MathLover1)
1.how do I factor: 3x^4-24xy^3 2. solve all complex roots: 9x^4-18x^3+3x^2=16x (answered by edjones)