Factoring Polynomials

[379furl379]

I can not remember how to factor polynomials at all. I learned it but I just don't remeber how. I started the problems, but I am pretty sure they are wrong, and I dont know where to go from here. So if someone can help it would be greatly appreciated.

#1 z^3 + 7z + 7z^2 + 7
z^3 + z^2 + 7z + 7
(z + 7)
I have no idea....

#2 2x^3 + 2x^2 - 84x
2x( x^2 + x - 42)
2x( x - 7)(x + 6)

#3 -4x^2 - 23x + 6
I think this one is prime....

#4 9xy^2 - 16x
x ( 9y^2 - 16)
x( 3y + 4)( 3y - 4)

#5 Solve: x^2 - 13x = -36
(x + 13)(x - 13) = -36
x + 13 = -36 x - 13 =-36
-13 -13 +13 +13
x = -49 or x = -23

And again I thank you If you can be of any help at all! Thank you!

 

[soroban]

Hello, 379furl379!

\(\displaystyle 1)\;\;z^3 + 7z + 7z^2 + 7\) . Is there a typo? This can't be factored.

\(\displaystyle 2)\;\;2x^3 + 2x^2 - 84x\)

\(\displaystyle 2x(x^2 + x - 42) \:=\:2x(x - 7)(x + 6)\)
. . . . . . . . . . . . . . . . .\(\displaystyle \uparrow\qquad\;\;\uparrow\)
. . . . . . . . . . . . . . \(\displaystyle ^{\text{signs are reversed}}\)

\(\displaystyle 3)\; -4x^2 - 23x + 6\)
I think this one is prime . . . . no

\(\displaystyle \text{Factor out -1: }\;-(4x^2 + 23x - 6) \;=\;-(x + 6)(4x - 1)\)

\(\displaystyle 4)\;9xy^2 - 16x\)

\(\displaystyle x(9y^2 - 16) \:=\:x(3y + 4)(3y - 4)\) . . . . Good!

\(\displaystyle 5)\;\text{Solve: }\:x^2 - 13x \:= \:-36\)

\(\displaystyle (x + 13)(x - 13) \:=\: -36\) . . . . no

\(\displaystyle \text{First, "Get everything on one side": }\:x^2-13x + 36 \:=\:0\)

. . \(\displaystyle \text{Factor: }\x-4)(x-9) \:=\:0\)

. . \(\displaystyle \text{Therefore: }\:x\:=\:4,\:9\)

 

[379furl379]

#1 is supossed to be: z^3 + 7z + z^2 + 7

sorry about that! And thanks for the help on the other problems!

 

[stapel]

I can not remember how to factor polynomials at all.

To re-learn the material, try some online lessons!

. . . . .Google results for "simple factoring"
. . . . .Google results for "factoring quadratics"
. . . . .Google results for "factoring trinomials"
. . . . .Google results for "special factoring"
. . . . .Google results for "factoring polynomials"

Have fun! :wink:

 

[379furl379]

Thanks those sites helped a lot!