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Math Help - Factoring

  1. #1
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    Factoring

    Can anyone factor this please. i'm bad on factoring polynomials.

    6x^3+17x^2+x-10


    thanks...
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  2. #2
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    Quote Originally Posted by Anemori View Post
    Can anyone factor this please. i'm bad on factoring polynomials.

    6x^3+17x^2+x-10


    thanks...
    6x^3+17x^2=10-x

    x^2(6x+17)=10-x

    x^2=\frac{10-x}{6x+17}

    Positive integers are unhelpful here, but if x=-1<br />

    1=\frac{11}{11}

    hence x=-1 is a solution, so [x-(-1)]=(x+1) is a factor.

    (x+1)(ax^2+bx+c)=6x^3+17x^2+x-10

    a=6, c=-10

    ax^3+bx^2+cx+ax^2+bx+c=ax^3+(a+b)x^2+(b+c)x+c=6x^3  +17x^2+x-10

    Hence, a+b=17, b=17-a=17-6=11

    or b+c=1, b-10=1, b=10+1=11

    Using this technique, "a" and "c" are found immediately,
    "b" can be found from either of the other two co-efficients using "a" or "c".

    6x^3+17x^2+x-10=(x+1)\left(6x^2+11x-10\right)

    The quadratic is easier to factorise.

    We get

    6x^3+17x^2+11x-10=(x+1)(3x-2)(2x+5)
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  3. #3
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    Quote Originally Posted by Archie Meade View Post
    6x^3+17x^2=10-x

    x^2(6x+17)=10-x

    x^2=\frac{10-x}{6x+17}

    Positive integers are unhelpful here, but if x=-1<br />

    1=\frac{11}{11}

    hence x=-1 is a solution, so [x-(-1)]=(x+1) is a factor.

    (x+1)(ax^2+bx+c)=6x^3+17x^2+x-10

    a=6, c=-10

    ax^3+bx^2+cx+ax^2+bx+c=ax^3+(a+b)x^2+(b+c)x+c=6x^3  +17x^2+x-10

    Hence, a+b=17, b=17-a=17-6=11

    or b+c=1, b-10=1, b=10+1=11

    Using this technique, "a" and "c" are found immediately,
    "b" can be found from either of the other two co-efficients using "a" or "c".

    6x^3+17x^2+x-10=(x+1)\left(6x^2+11x-10\right)

    The quadratic is easier to factorise.

    We get

    6x^3+17x^2+11x-10=(x+1)(3x-2)(2x+5)
    oh ok thanks....
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  4. #4
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    Quote Originally Posted by Anemori View Post
    Can anyone factor this please. i'm bad on factoring polynomials.

    6x^3+17x^2+x-10


    thanks...
    By inspection x = -1 is a zero of 6x^3+17x^2+x-10 and so x + 1 is a factor. Now divide x + 1 into 6x^3+17x^2+x-10 to get the quadratic factor and then factorise (if possible) the quadratic.
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