x^3 + 9x^2 + 26x + 24 how would i solve this?!?

x³ + 9x² + 26x + 24
= x² + 4x² + 5x² + 20x + 6x + 24
= x²(x + 4) + 5x(x + 4) +6(x + 4)
= (x + 4)(x² + 5x + 6)
= (x + 4)(x + 3)(x + 2)
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x^3 + 9x^2 + 26x + 24=x^3+4x^2+5x^2+20x+6x+24=


x^2(x+4)+5x(x+4)+6(x+4)=(x+4)(x^2+5x+6)=

(x+4)(x+2)(x+3)=0 x=-4 x=-2 x=-3

x^3 + 9x^2 + 26x + 24
= (x^2 + 5x + 6)(x + 4)
= (x + 3)(x + 2)(x + 4)

for me, the easiest and sure way is by the use of the synthetic division. it goes like this:
we get the numerical coefficient of each term,
1...9...26...24
then we think of a number, say 1, or 2, or 3, or their negatives, just those small ones.. say i like -2, first we bring down the first numerical coefficient:
1...9...26...24

1
then we multiply it by our chosen number which is -2, then we write it below the second numerical coefficient, then add:
1...9...26...24
....-2...
1...7
then continue the step til the last coefficient:
1...9...26...24
....-2..-14..-24
1...7...12....0.
the last number should be zero. if you got 0 on the last, then you made the right choice. -2 is one of the factors. then those reamining coefficients will be the coefficient of your new polynomial which have the degree next to the highest degree that you solved earlier. now it's:
x^2 + 7x + 12 = 0
then solve it using factoring method:
(x + 3) * (x + 4) = 0
x = -3 and x = -4
you already have the solution that is x = -2, -3, and -4.

hope it hepled. ^_^

By trial and error, -4,-3,-2 are the roots

There is the easy way and the hard way. The easy way involves graphing it on a graphing calculator and seeing where it intersects the x-axis. On the Ti's, you can press 2nd and trace=calc (at the top). The 2nd option is the zero function and you have to press the cursor at the left and right of intersections and it will tell you the answer. The hard way involves using synthetic division where you plug in values until you get something without a remainder. Instead of explaining it, I'll direct you to some place that does:
http://www.purplemath.com/modules/synthdiv.htm

x^3 + 9x^2 + 26x + 24 = (x + 4)(x² + 5x + 6)
. . . . . . . . . . . . . . . . . . . = (x + 4)(x + 2)(x + 3)


Alejandra