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Math Help - Factorizing - a true headache

  1. #1
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    Unhappy Factorizing - a true headache

    please someone help: penultimate question one of my step paper quizzes;

    8x3+6x2-23x+9 or in other words:

    Reduce to a binomial expression the sum of eight times a number x raised to the power of three and six times a number x raised to the power of two less the sum of twenty three times a number x and 9.
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  2. #2
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    Why not just use the '^' symbol to represent powers?. That's what it's for.

    Anyway, there are various ways to tackle these. The Rational Root Theorem is always a choice if it's a toughy.

    You can also break it up:

    8x^{3}+6x^{2}-23x+9

    Break it up:

    8x^{3}+18x^{2}-12x^{2}-27x+4x+9

    Group and factor:

    (8x^{3}-12x^{2}+4x)+(18x^{2}-27x+9)

    Factor:

    4x(2x^{2}-3x+1)+9(2x^{2}-3x+1)

    See?. What's in the parentheses is the same.

    (4x+9)(2x^{2}-3x+1)

    Now, the quadratic factors as well. Finish up.
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