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21 March, 17:51

What is the remainder when 2x^3+3x^2+x+1 is divided by x+3

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  1. 21 March, 18:06
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    2x^3 + 3x^2 + x + 1

    =2x^3 + 3x^2 + 3x^2 - 3x^2 + x + 1

    =2x^3 + 6x^2 - 3x^2 + x + 1

    =2 (x^3 + 3x^2) - 3x^2 + x + 1

    =2x^2 * (x+3) - 3x^2 - 9x + 9x + x + 1

    =2x^2 * (x+3) - 3x (x+3) + 10x + 1

    =2x^2 * (x+3) - 3x (x+3) + 10x + 30 - 30 + 1

    =2x^2 * (x+3) - 3x (x+3) + 10 (x+3) - 29

    The first three terms can be divided by (x+3) evenly so the remainder is - 29
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