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factoring polynomials help?

posted by on .

16x^4-1

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? - ,

    1. 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? - ,

    2. 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? - ,

    Unless 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? - ,

    #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? - ,

    You're welcome!

  • factoring polynomials help? - ,

    5p^2+14p+8

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