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Math

Question

find the remainder when x cube minus 3 X square + 3 x minus 1 is divided by X + 3​

1 Answer

  • GIVEN

    [tex]p(x) = {x}^{3} - 3 {x}^{2} + 3x - 1[/tex]

    [tex]g(x) = x + 3[/tex]

    TO FIND :- Remainder of P(x) ÷ g(x)

    SOLUTION

    We can solve it by division algorithm as given in the attachment.

    But we can go for Remainder Theorem for such questions :-

    By remainder Theorem we have to find zero of g(x)

    g(x) = x + 3

    => x + 3 = 0

    => x = -3

    We have to simply insert the value of x in p(x) to get the remainder :-

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

    p( - 3) = ( - 3)^3 - 3 × (-3)^2 + 3 × -3 -1

    = - 27 - 3 × 9 - 9 -1

    = - 27 - 27 - 9 -1

    = - 64

    Hence the remainder is -64.

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