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August 21, 2014

Posted by **Skye** on Sunday, November 6, 2011 at 7:16pm.

4x^4+39x^2-10

find the real number solutions of these equations.

3x^4+15x^2-72=0

x^3+2x^2-x=0

Thanks!

- factoring polynomials help? -
**Henry**, Sunday, November 6, 2011 at 9:03pm1. 16x^4 - 1 =

(4x^2+1)(4x^2-1) =

(4x^2+1)(2x+1)(2x-1).

2.

3. 3x^4 + 15x^2 - 72 = 0,

X = +- 2.19.

EXCEL Spreadsheets were used.

4. x^3 + 2x^2 - x = 0,

X= 0.

- factoring polynomials help? -
**Henry**, Sunday, November 6, 2011 at 9:23pm2. 4x^4 + 39x^2 - 10 = 0.

AC Method:

A*C = 4*(-10) = -40 = -1*40.

4x^4 + (-x^2+40x^2) -10,

Group terms into factorable pairs:

(4x^4 - x^2) + (40x^2-10) =

x^2(4x^2-1) + 10(4x^2-1) =

4x^2-1(x^2+10) =

(2x+1)(2x-1)(x^2+10).

- factoring polynomials help? -
**MathMate**, Sunday, November 6, 2011 at 9:30pmUnless I am mistaken, you may want to check the EXCEL spreadsheet results.

#3

3x^4+15x^2-72=0 factors well to

3(x^2-3)(x^2+8)=0

which gives

x=±sqrt(3) or

x=±(2√2)i

and #4

x^3+2x^2-x=0

factors into

x(x^2+2x-1)

which gives x=0, or

x=(-2±√(2^2+4))/2

=-1±√8

=-1±2√2

- factoring polynomials help? -
**Henry**, Sunday, November 6, 2011 at 10:28pm#3. Your procedure was easy to follow:

I will use it on similar problems.

EXCEL doesn't work properly when imaginary numbers are involved.

Thanks for the INFO!

- factoring polynomials help? -
**MathMate**, Monday, November 7, 2011 at 10:26pmYou're welcome!

- factoring polynomials help? -
**Emily**, Friday, October 5, 2012 at 8:38pm5p^2+14p+8

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