how do i solve p(x)=x(x+3)^3(x-3)?

the answer is x^5+6x^4-54x^2-81x. i need the process broken down on how to get the answer.

4 Answers

Relevance
  • 1 decade ago
    Favorite Answer

    p(x) = x(x+3)^3(x-3)

    First I will rearrange to make things a little easier.

    p(x) = x(x-3)(x+3)^3

    Now to write the (x+3)^3 as a series of multiplications. I will also multiply the first two factors together as well.

    p(x) = (x^2 - 3x)(x+3)(x+3)(x+3)

    Expand the (x+3)(x+3) by multiplying it together, using FOIL.

    p(x) = (x^2 - 3x)(x^2 + 3x +3x + 9)(x+3)

    Simplify.

    p(x) = (x^2 - 3x)(x^2 + 6x + 9)(x+3)

    Multiply (x^2 + 6x + 9)(x+3) together.

    p(x) = (x^2 - 3x)(x^3 + 6x^2 + 9x + 3x^2 + 18x + 27)

    Simplify.

    p(x) = (x^2 - 3x)(x^3 + 9x^2 + 27x + 27)

    Expand.

    p(x) = x^5 - 3x^4 + 9x^4 - 27x^3 + 27x^3 - 81x^2 + 27x^2 - 81x

    Simplify.

    p(x) = x^5 - 6x^4 + 0x^3 - 54x^2 - 81x

    Eliminate the 0 term.

    p(x) = x^5 - 6x^4 - 54x^2 - 81x

    And there you go.

  • Anonymous
    1 decade ago

    Do it piece by piece.

    1) (x + 3)^3 = x^3 + 9x^2 + 27x + 27

    2) (x - 3)(x^3 + 9x^2 + 27x + 27) = x^4 + 6x^3 - 54x - 81

    3) x(x^4 + 6x^3 - 54x - 81) = x^5 + 6x^4 - 54x^2 - 81x

    See how easy?

    :)

  • Anonymous
    1 decade ago

    (x+3)(x+3)(x+3) = x^3 + 9x^2 +27x + 27

    (x^3 + 9x^2 +27x + 27)times x = x^4 + 9x^3 +27x^2 + 27x

    (x^4 + 9x^3 +27x^2 + 27x)(x-3) = x^5 + 6x^4 -54x^2 - 81x

  • 1 decade ago

    Well first you begin with the part (x+3)^3

    it will be easier to just do (x+3)^2 get the answer to that and then multiply it again by (x+3)

    after that step you should get x^3+6x^2+9x+3x^2+18x+27

    group like terms then multiply that by the first X

    x(x^3+9x^2+27x+27) Distribute the x to all terms

    =(x^4+9x^3+27x^2+27^x)

    Take that and distribute (x-3) to all terms

    group like terms and you should get that answer.

    hope that helps

Still have questions? Get your answers by asking now.