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15 November, 10:09

Given one factor of the polynomial, factor the polynomial completely.

16. f (x) = x^3-4x^2-7x+10; x-5

17. g (x) = 2x^3+3x^2-23x-12; 2x+1

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  1. 15 November, 13:21
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    Use synthetic division to solve these problems

    5 | 1 - 4 - 7 10

    | v 5 5 - 10

    1 1 - 2 0

    This leads to x^2+x-2

    Next we find what adds to 1 and multiplies to - 2

    The factors of f (x) are 2 and - 1, written out as (x+2) and (x-1)

    -1/2 | 2 3 - 23 - 12

    | v - 1 - 1 12

    2 2 - 24 0

    This leads to 2x^2+2x-24

    Next, multiply the 2 from the a value (since a is the value with x^2 and c is the value without any x) with - 24, which is - 48

    Now find what adds to 2 and multiplies to - 48

    The values for this are 8 and - 6, but keep in mind, when multiplying the value of a by c, you now have to add the values in place of what you tried adding it to, this time in the problem we found using synthetic division, in this case the 2 in the b value (the middle of the equation, or the value with only one x)

    2x^2+8x-6x-24

    When group factoring, you'd get 2x (x+4) - 6 (x+4)

    So, the factors of g (x) are (x+4) and (2x-6)
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